Lenz's Law Explained


Lenz’s Law is a principle of electromagnetic induction stating that induced current flows in a direction that opposes the change in magnetic flux producing it. This rule ensures energy conservation and explains how circuits, coils, generators, and transformers behave in changing fields.

 

What is Lenz’s Law?

Lenz’s Law, rooted in Faraday’s Law of Induction, states that the direction of an induced current or electromotive force (emf) always opposes the change in magnetic flux that produced it. This principle safeguards conservation of energy in electromagnetic systems.

✅ Explains opposing force in induced current and magnetic fields

✅ Fundamental to understanding circuits, transformers, and generators

✅ Practical in energy conversion, electric motors, and induction device

Lenz's Law, named after the Russian physicist Heinrich Lenz (1804-1865), is a fundamental principle in electromagnetism. It states that the direction of the induced electromotive force (emf) in a closed conducting loop always opposes the change in magnetic flux that caused it. This means that the induced current creates a magnetic field that opposes the initial change in magnetic flux, following the principles of conservation of energy. A strong grounding in basic electricity concepts makes it easier to see why Lenz’s Law is central to modern circuit design.

 


 

Understanding Lenz's Law enables us to appreciate the science behind various everyday applications, including electric generators, motors, inductors, and transformers. By exploring the principles of Lenz's Law, we gain insight into the inner workings of the electromagnetic world that surrounds us. Engineers use this principle when designing three-phase electricity systems and 3-phase power networks to maintain energy balance.

Lenz's Law, named after the Russian physicist Heinrich Lenz (1804-1865), is a fundamental principle that governs electromagnetic induction. It states that the induced electromotive force (emf) in a closed conducting loop always opposes the change in magnetic flux that caused it. In simpler terms, the direction of the induced current creates a magnetic field that opposes the initial change in magnetic flux. 

Lenz's Law is a fundamental law of electromagnetism that states that the direction of an induced electromotive force (EMF) in a circuit is always such that it opposes the change that produced it. Mathematically, Lenz's Law can be expressed as:

EMF = -dΦ/dt

Where EMF is the electromotive force, Φ is the magnetic flux, and dt is the change in time. The negative sign in the equation indicates that the induced EMF is in the opposite direction to the change in flux.

Lenz's Law is closely related to Faraday's Law of electromagnetic induction, which states that a changing magnetic field induces an EMF in a circuit. Faraday's Law can be expressed mathematically as:

EMF = -dΦ/dt

where EMF is the electromotive force, Φ is the magnetic flux, and dt is the change in time.

Ampere's Law and the Biot-Savart Law are also related to Lenz's Law, as they describe the behaviour of electric and magnetic fields in the presence of currents and charges. Ampere's Law states that the magnetic field around a current-carrying wire is proportional to the current and the distance from the wire. The Biot-Savart Law describes the magnetic field produced by a current-carrying wire or a group of wires. Because Lenz’s Law governs the behavior of induced currents, it directly complements Ampere’s Law and the Biot-Savart Law in explaining magnetic fields.

Together, these laws provide a complete description of the behaviour of electric and magnetic fields in various situations. As a result, they are essential for understanding the operation of electric motors, generators, transformers, and other devices.

To better understand Lenz's Law, consider the scenario of a bar magnet moving toward a coil of wire. When the magnet moves closer to the coil, the number of magnetic field lines passing through the coil increases. According to Lenz's Law, the polarity of the induced emf in the coil is such that it opposes the increase in magnetic flux. This opposition creates an induced field that opposes the magnet's motion, ultimately slowing it down. Similarly, when the magnet is moved away from the coil, the induced emf opposes the decrease in magnetic flux, creating an induced field that tries to keep the magnet in place.

The induced field that opposes the change in magnetic flux follows the right-hand rule. If we hold our right hand around the coil such that our fingers point in the direction of the magnetic field lines, our thumb will point in the direction of the induced current. The direction of the induced current is such that it creates a magnetic field that opposes the change in the magnetic flux.

The pole of the magnet also plays a crucial role in Lenz's Law. When the magnet's north pole moves towards the coil, the induced current creates a magnetic field that opposes the north pole's approach. Conversely, when the magnet's south pole moves towards the coil, the induced current creates a magnetic field that opposes the south pole's approach. The direction of the induced current follows the right-hand rule, as we discussed earlier.

It is related to Faraday's Law of Electromagnetic Induction, which explains how a changing magnetic field can induce an electromotive force (emf) in a conductor. Faraday's Law mathematically describes the relationship between the induced electromotive force (emf) and the rate of change of magnetic flux. It follows Faraday's Law, as it governs the direction of the induced emf in response to the changing magnetic flux. To fully understand how electromagnetic induction works, it is helpful to see how Faraday’s discoveries laid the foundation for Lenz’s Law.

It is also related to the phenomenon of eddy currents. Eddy currents are loops of electric current induced within conductors by a changing magnetic field. The circulating flow of these currents generates their magnetic field, which opposes the initial magnetic field that created them. This effect is in line with Lenz's Law and has practical applications, such as in the braking systems of trains and induction cooktops.

Lenz's Law has numerous practical applications in our daily lives. For example, it plays a significant role in the design and function of electric generators, which convert mechanical energy into electrical energy. In a generator, a rotating coil experiences a changing magnetic field, resulting in the generation of an electromotive force (emf). The direction of this induced emf is determined by Lenz's Law, which ensures that the system conserves energy. Similarly, electric motors operate based on Lenz's Law. In an electric motor, the interaction between the magnetic fields and the induced electromotive force (emf) creates a torque that drives the motor. In transformers, including 3-phase padmounted transformers, Lenz’s Law explains why flux changes are controlled for efficiency and safety.

Lenz's Law is an essential concept in the design of inductors and transformers. Inductors are electronic components that store energy in their magnetic field when a current flows through them. They oppose any change in the current, following the principles of Lenz's Law. Transformers, which are used to transfer electrical energy between circuits, utilize the phenomenon of electromagnetic induction. By understanding it, engineers can design transformers.

 

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Electricity Terms Explained

Electricity terms explain voltage, current, resistance, impedance, power factor, frequency, AC/DC, circuits, transformers, and load. Master key definitions to analyze systems, size conductors, mitigate harmonics, and ensure safety compliance.

 

Understanding Electricity Terms in Electrical Safety

Here are the top 50 commonly used electricity terms that are essential for understanding electrical systems, devices, and concepts: For a broader glossary with context and examples, see the curated list at Electrical Terms by Electricity Forum for deeper reference.

Voltage (V) – The electrical potential difference between two points in a circuit. Understanding how potential difference relates to the nature of electricity is clarified in this overview of what electricity is and how it behaves.

Current (I) – The flow of electric charge, measured in amperes (A). A concise explanation of electricity as a physical phenomenon is given in this definition of electricity for foundational understanding.

Resistance (R) – Opposition to current flow, measured in ohms (Ω).

Power (P) – The rate of doing work or transferring energy, measured in watts (W).

Ohm's Law – The relationship between voltage, current, and resistance. For a step-by-step refresher on the relationships among voltage, current, and resistance, explore this basic electricity guide to connect theory with practical examples.

Alternating Current (AC) – Electric current that reverses direction periodically.

Direct Current (DC) – Electric current that flows in one direction only. For a side-by-side comparison of waveform behavior, applications, and conversion methods, review the differences between AC and DC to strengthen conceptual understanding.

Frequency (f) – The number of cycles per second in AC, measured in hertz (Hz).

Impedance (Z) – The total opposition to current flow in an AC circuit, combining resistance and reactance, measured in ohms.

Capacitance (C) – The ability to store electrical energy in an electric field, measured in farads (F).

Inductance (L) – The ability of a conductor to induce a voltage when current changes, measured in henries (H).

Power Factor (PF) – The ratio of real power to apparent power, indicating the efficiency of a system.

Real Power (P) – The actual power consumed to perform work, measured in watts.

Apparent Power (S) – The total power in a system, combining real and reactive power, measured in volt-amperes (VA).

Reactive Power (Q) – Power in AC circuits that does not perform useful work, measured in volt-amperes reactive (VAR).

Load – The device or equipment that consumes electrical power.

Short Circuit – An abnormal connection between two points in a circuit, causing excessive current flow. To ground this topic in fundamentals, revisit what an electrical circuit is before examining fault conditions.

Overload – A condition where a circuit or device exceeds its rated current capacity.

Circuit Breaker – A protective device that interrupts the flow of current when an overload or short circuit occurs.

Fuse – A protective device that melts to break the circuit when excessive current flows.

Grounding (Earthing) – Connecting parts of an electrical system to the Earth to ensure safety.

Transformer – A device that transfers electrical energy between two or more circuits through electromagnetic induction.

Conductor – A material that allows the flow of electrical current, typically copper or aluminum.

Insulator – A material that resists the flow of electric current, such as rubber or plastic.

Phase – The distribution of alternating current electricity into separate waveforms, often used in three-phase power systems.

Watt (W) – The unit of power, equivalent to one joule per second.

Kilowatt (kW) – A unit of power equal to 1,000 watts.

Megawatt (MW) – A unit of power equal to 1 million watts.

Voltage Drop – The reduction in voltage across a component or conductor in an electrical circuit.

Arc Flash – A dangerous condition associated with the release of energy caused by an electric arc.

Resistor – A component that opposes the flow of current, used to control voltage and current in circuits.

Diode – A semiconductor device that allows current to flow in one direction only.

Rectifier – A device that converts AC to DC.

Inverter – A device that converts DC to AC.

Contactor – An electrically controlled switch used to control a power circuit.

Relay – A switch operated by an electromagnet, used for controlling circuits.

Switchgear – Equipment used to switch, control, and protect electrical circuits.

Distribution System – The system of wires and equipment that delivers electricity from substations to consumers.

Neutral – A conductor that carries current back to the source in an electrical system.

Busbar – A conductor used to distribute power from one source to multiple circuits.

Overcurrent Protection – Devices like fuses and circuit breakers designed to protect circuits from excessive current.

Phase Angle – The angular displacement between voltage and current waveforms in AC circuits.

Power Supply – A device that provides the necessary electrical power to a circuit or device.

Generator – A device that converts mechanical energy into electrical energy. This ties directly to how electrical energy is produced, transferred, and ultimately consumed.

Motor – A device that converts electrical energy into mechanical energy.

Frequency Converter – A device that changes the frequency of AC power.

Power Grid – A network of transmission lines, substations, and power stations for distributing electricity.

Service Panel – The central distribution point for electrical circuits in a building, containing circuit breakers or fuses.

Utility Transformer – A transformer that steps down high voltage for distribution to consumers.

Harmonics – Distortions in the electrical waveform that can affect power quality.

These terms cover a wide range of concepts from basic electrical theory to components and safety practices in electrical systems.
 

 

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Definition of a Rectifier

Definition of a rectifier explains AC to DC conversion using diodes, bridge or full-wave circuits, filters, and regulators to supply stable DC, reduce ripple, and power electronics, chargers, and DC motor drives.

 

Key Concepts of the Definition of a Rectifier

Understanding the definition of a rectifier is fundamental to grasping the complexities of power electronics and electrical engineering. Rectifiers are pivotal in converting AC power to DC power, a critical process for operating numerous electronic devices. By delving into the intricacies of half-wave, full-wave, and bridge rectifiers, as well as the silicon-controlled rectifier, it becomes clear that these devices are crucial in shaping the modern world of electronics. For readers new to the basics, an overview of the difference between AC and DC can clarify foundational concepts.


 

In electrical engineering, the definition encompasses a vital device that plays a crucial role in converting alternating current (AC) into direct current (DC). It  is an essential component in power electronics. It facilitates the conversion of AC power, commonly used in households and businesses, to DC power that electronic devices rely on. To contextualize this conversion, understanding alternating current behavior in typical distribution systems explains the need for rectification.

They come in various forms, such as diodes, mercury arc valves, and silicon-controlled rectifiers (SCRs). A diode, the most basic rectifying component, allows current to flow in only one direction. This feature helps convert AC power, which alternates direction, to DC power that flows in a single, continuous direction. For measurement and notation conventions, see how DC current is defined and applied in circuit analysis.

AC to DC conversion regulates voltage to create a steady and reliable energy supply. Throughout this conversion, rectifiers often assume different configurations depending on the specific application or requirement. Two popular configurations are the half-wave rectifier and the full-wave rectifier. Downstream stabilization is often handled by a voltage regulator that smooths residual ripple and safeguards loads.

A half-wave type allows only one half of the AC waveform to pass through while blocking the other half. This type is relatively simple and cost-effective but has a few downsides, such as lower efficiency and increased ripple voltage. Ripple voltage refers to the residual periodic variation of the DC output voltage. The result is an unsteady DC output, which might be undesirable in certain applications.

On the other hand, the full-wave type allows both halves of the AC waveform to pass through, effectively doubling the output frequency and reducing the ripple voltage. This configuration improves efficiency and provides a smoother, more consistent DC output voltage. The full-wave type has two primary forms: the center-tap configuration and the bridge rectifier.

The bridge rectifier is a highly efficient configuration that uses four diodes in a specific arrangement. This configuration eliminates the need for a center-tapped transformer, a key component in center-tap full-wave rectifiers, thus reducing overall size and cost. In addition, the bridge rectifier provides better voltage regulation and reduced harmonic distortion, making it ideal for various applications. For consistent terminology across datasheets, reviewing key electricity terms can prevent misinterpretation during design.

They serve numerous purposes in various fields. For instance, they are used in power supply circuits of electronic devices, battery chargers, and welding equipment. In addition, they help in voltage regulation for DC power supplies and extract radio signals from transmitted modulated signals. Many of these uses depend on stable direct current characteristics to ensure predictable device behavior.

Silicon-controlled rectifiers (SCRs) represent a more advanced type of rectifier. As silicon-based semiconductor switches, SCRs can control large amounts of current with a small input signal. This ability to manage current flow in a controlled manner sets SCRs apart from regular rectifiers, like diodes. As a result, SCRs are often used in power control applications, such as motor speed controllers, light dimmers, and temperature regulators.

Understanding how rectifiers play a pivotal role in industries and everyday applications is essential. One such application is in electric vehicles (EVs), where rectifiers contribute to charging systems by converting AC power from the grid to DC power for charging the battery. Additionally, they are utilized in renewable energy systems, like solar power and wind power, to convert the harvested energy into a stable and usable form for various applications. At a broader level, a concise electricity definition helps frame how conversion stages integrate with generation, storage, and loads.

Another application is in telecommunications equipment, where they help maintain a continuous and stable power supply. In the aviation and marine industries, rectifiers ensure sensitive equipment operates with minimal interference from fluctuating power sources. Moreover, they are employed in power supply units of medical devices, computers, and other critical equipment that demand stable power supplies.


How does it work in AC to DC conversion?

Its primary function is to convert AC voltage, which periodically reverses direction, into DC voltage, which flows in one direction. Its simplest form it consists of a diode, which allows current to pass in only one direction. When connected to an AC power source, the diode rectifies the current by blocking the negative half-cycles of the AC waveform. More advanced configurations, like full-wave rectifiers and bridge rectifiers, rectify both the positive and negative half-cycles, increasing efficiency and providing a smoother output.


What are the differences between half-wave and full-wave rectifiers?

The key difference between half-wave and full-wave rectifiers lies in their efficiency and output. A half-wave type only allows one-half of the AC waveform to pass through, blocking the other half. As a result, it has lower efficiency, increased ripple voltage, and produces an unsteady DC output.

On the other hand, a full-wave type allows both halves of the AC waveform to pass through, leading to increased efficiency and reduced ripple voltage. In addition, the full-wave type produces a smoother, more consistent DC output voltage, making it more suitable for applications that require a stable power supply. The full-wave type can be implemented using a center-tap or bridge rectifier configuration.

 

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Geothermal Electricity Explained

Geothermal electricity delivers renewable baseload power by converting subsurface heat through turbines, generators, ORC binary cycles, and heat exchangers, enabling grid integration, high capacity factor, low emissions, and efficient power plant control systems.

 

Understanding How Geothermal Electricity Works

Geothermal Electricity is produced through geothermal power plants capturing the thermal energy contained in the Earth. Use of geothermal energy is based thermodynamically on the temperature difference between a mass of subsurface rock and water and a mass of water or air at the Earth's surface. This temperature difference allows production of thermal energy that can be either used directly or converted to mechanical or Geothermal Electricity. For context on broader methods and terminology, see this overview of electricity generation and how heat energy is converted to power.

Commercial exploration and development of Plant Geothermal water generated into Electricity to date have focused on natural geothermal reservoirs—volumes of rock at high temperatures (up to 662°F or 350°C) and with both high porosity (pore space, usually filled with water) and high permeability (ability to transmit fluid). The thermal energy is tapped by drilling wells into the reservoirs. The thermal energy in the rock is transferred by conduction to the fluid, which subsequently flows to the well and then to the Earth's surface where it can be converted into Geothermal Electricity. This well-to-turbine pathway is a fundamental part of electricity production from thermal resources.

There are several types of natural geothermal reservoirs. All the reservoirs developed to date for electrical energy are termed hydrothermal convection systems and are characterized by circulation of meteoric (surface) water to depth. The driving force of the convection systems is gravity, effective because of the density difference between cold, downward-moving, recharge water and heated, upward-moving, thermal water. A hydrothermal convection system can be driven either by an underlying young igneous intrusion or by merely deep circulation of water along faults and fractures. Depending on the physical state of the pore fluid, there are two kinds of hydrothermal convection systems: liquid-dominated, in which all the pores and fractures are filled with liquid water that exists at temperatures well above boiling at atmospheric pressure, owing to the pressure of overlying water; and vapor-dominated, in which the larger pores and fractures are filled with steam. Liquid-dominated reservoirs produce either water or a mixture of water and steam, whereas vapor-dominated reservoirs produce only steam, in most cases superheated. Because water acts as the primary working fluid in most systems, understanding the interplay of water and electricity helps clarify operational safety and design.

These hydrothermal systems are distinct from hydroelectricity produced by river impoundments, even though both ultimately rely on water as a medium.

Although geothermal energy is present everywhere beneath the Earth's surface, its use is possible only when certain conditions are met: (1) The energy must be accessible to drilling, usually at depths of less than 2 mi (3 km) but possibly at depths of 4mi (6–7km) in particularly favorable environments (such as in the northern Gulf of Mexico Basin of the United States). (2) Pending demonstration of the technology and economics for fracturing and producing energy from rock of low permeability, the reservoir porosity and permeability must be sufficiently high to allow production of large quantities of thermal water. (3) Since a major cost in geothermal development is drilling and since costs per meter increase with increasing depth, the shallower the concentration of geothermal energy the better. (4) Geothermal fluids can be transported economically by pipeline on the Earth's surface only a few tens of kilometers, and thus any generating or direct-use facility must be located at or near the geothermal anomaly. When these conditions align, engineered systems can efficiently generate electricity from accessible geothermal gradients.

The use of geothermal energy for Geothermal Electricity has become widespread because of several factors. Countries where geothermal resources are prevalent have desired to develop their own resources in contrast to importing fuel for power generation. In countries where many resource alternatives are available for power generation, including geothermal, geothermal has been a preferred resource because it cannot be transported for sale, and the use of geothermal energy enables fossil fuels to be used for higher and better purposes than power generation. Also, geothermal steam has become an attractive power generation alternative because of environmental benefits and because the unit sizes are small (normally less than 100 MW). Moreover, geothermal plants can be built much more rapidly than plants using fossil fuel and nuclear resources, which, for economic purposes, have to be very large in size. Electrical utility systems are also more reliable if their power sources are not concentrated in a small number of large units. In energy planning, geothermal is often evaluated alongside other forms of alternative electricity to balance portfolios and grid resilience. Many developers also highlight its contribution to green electricity targets thanks to low lifecycle emissions.

 

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Watthour Meter Explained

A watthour meter measures electrical energy consumption in kilowatt-hours (kWh) for residential, commercial, and industrial applications, ensuring accurate billing, energy management, and compliance with utility standards.

 

What is a Watthour Meter?

✅ Measures total electrical energy in kilowatt-hours (kWh) over time

✅ Supports accurate billing, energy monitoring, and demand analysis

✅ Used in residential, commercial, and industrial revenue metering

 

Advancements in Watthour Meter Technology and Energy Measurement

Watthour meter technology plays a crucial role in modern electrical engineering and maintenance by providing accurate measurement and monitoring of energy consumption. These devices are indispensable for managing energy efficiency, optimizing power distribution, and ensuring compliance with regulatory standards. For electrical professionals, understanding how they operate and are maintained is essential to minimize energy losses and enhance the reliability of electrical systems. With the growing demand for precise energy data in both residential and industrial applications, staying informed about advancements in watthour meter technology is more important than ever. Understanding how a watthour is calculated helps clarify how a watthour meter tracks total energy usage for accurate billing. 

 

How Induction Type Single Phase Watt Hour Meters Work

Induction type meters, commonly used as single phase watt hour meters, provide accurate measurement of electrical energy consumption in residential and small commercial installations.

Your electric utility is not too interested in how much power you're consuming for one ap­pliance or even how much power a single household is drawing at any given time. By far the greater concern is the total energy that is used over a day, a week, a month or a year. Electrical energy is measured in watt-hours or, more commonly for utility pur­poses, in kilowatt-hours (kWh). The device that measures this consumption is the watt-hour meter or kilowatt-hour meter. For a deeper understanding of the units used in metering, see our guide on electrical energy and how it is measured in kilowatt-hours.

The most common method for measuring electrical energy is by using a small elec­tric motor device, whose speed depends on the current, and thereby on the power at a constant voltage. The number of turns of the motor shaft, in a given length of time, is di­rectly proportional to the number of watt hours consumed. The motor is placed at the point where the utility wires enter the house, apartment or building. This is usually at a point where the voltage is 234 V. This is split into some circuits with 234 V, for heavy-duty appliances such as the oven, washer and dryer, and the general household circuits for lamps, clock radios and television sets. The principles behind watthour meters are closely tied to basic electricity and the relationship between active power and time.

 

Understanding the Spinning Disk in Electromechanical Watthour Meters

You've surely seen the little disk in the utility meter going around and around, sometimes fast, other times slowly. Its speed depends on the power you're using. The total number of turns of this little disk, every month, determines the size of the bill you will get, as a function also, of course, of the cost per kilowatt hour for electricity.

Kilo-watt-hour meters count the number of disk turns by means of geared, rotary drums or pointers. The drum-type meter gives a direct digital readout. The pointer type has several scales calibrated from 0 to 9 in circles, some going clockwise and others go­ing counterclockwise. Mechanical and electronic meters both rely on the concepts of electrical resistance and current to provide precise readings.

 

How to Read a Pointer-Type Watthour Meter Accurately

Reading a pointer-type utility meter is a little tricky because you must think in whatever direction (clockwise or counterclockwise) the scale goes. An example of a pointer-type utility meter is shown in Fig. 3-11. Read from left to right. For each little meter, take down the number that the pointer has most recently passed. Write down the rest as you go. The meter in the figure reads 3875 kWh. If you want to be really pre­cise, you can say it reads 3875-1/2 kWh. To place watt hour metering in historical context, explore our history of electricity page and learn how early meters evolved into today’s advanced devices.

 


 

Fig. 3-11 An example of a utility kilo-watthour meter. The reading is a little more than 3875 kWh.

 

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Capacitors Explained

Capacitors store electrical energy via a dielectric, offering capacitance for filtering, smoothing, and decoupling in AC/DC circuits, RC networks, and power supplies, spanning ceramic, film, and electrolytic types with distinct impedance profiles.

 

The Science Behind Capacitors

Capacitors for Power Factor Correction

It is desirable to add shunt capacitors in the load area to supply the lagging component of current with a positive negative charging electrons. The cost is frequently justified by the value of circuit and substation capacity released and/or reduction in losses. Installed cost of shunt capacitors is usually least on primary distribution systems and in distribution substations. For foundational context, see what a capacitor is to understand reactive power roles.

The application of shunt capacitors to a distribution feeder produces a uniform voltage boost per unit of length of line, out to its point of application. Therefore, it should be located as far out on the distribution system as practical, close to the loads requiring the kilovars. There are some cases, particularly in underground distribution, where secondary capacitors are economically justified despite their higher cost per kilovar. The placement effectiveness also depends on capacitance characteristics relative to feeder impedance.

Development of low-cost switching equipment for capacitors has made it possible to correct the power factor to a high value during peak-load conditions without overcorrection during light-load periods. This makes it possible for switched capacitors to be used for supplementary voltage control. Time clocks, temperature, electric charge voltage, current flows, and kilovar controls are common actuators for high frequency capacitor switching. Utilities typically choose among several types of capacitors to balance switching duty and reliability.

Capacitor Installations

Capacitors for primary systems are available in 50- to 300-kvar single phase units suitable for pole mounting in banks of 3 to 12 units. Capacitors should be connected to the system through fuses so that a capacitor failure will not jeopardize system reliability or result in violent case rupture. When voltage ratings limit a single unit, engineers connect capacitors in series to distribute stress effectively.

 

Effect of Shunt Capacitors on Voltage

Proposed permanently connected capacitor applications should be checked to make sure that the voltage to some customers will not rise too high during light-load periods. Switched capacitor applications should be checked to determine that switching the capacitor bank on or off will not cause objectionable flicker in electronics. Selecting appropriate sizes in the standard unit of capacitance helps manage voltage rise and flicker.

 

Effect of Shunt Capacitors on Losses

The maximum loss reduction on a feeder with distributed load is obtained by locating positively negatively capacitor banks on the feeder where the capacitor kilovars is equal to twice the load kilovars beyond the point of installation. This principle holds whether one or more than one capacitor bank is applied to a feeder. To meet kvar targets with modular banks, utilities often add capacitance in parallel so reactive output scales predictably.

Capacitor kilovars up to 70% of the total kiovar load on the feeder can be applied as one bank with little sacrifice in the maximum feeder-loss discharge reduction possible with several capacitor banks.

A rule of thumb for locating a single capacitor bank on a feeder with uniformly distributed loads is that the maximum loss reduction can be obtained when the capacitor kilovars of the bank is equal to two-thirds of the kilovar load on the feeder. This bank should be located two-thirds of the distance out on the distributed feeder portion for object charging. Deviation of the capacitor bank location from the point of maximum loss reduction by as much as 10 per cent of the total feeder length does not appreciably affect the loss benefit. Therefore, in practice, in order to make the most out of the capacitor's loss reduction and voltage benefits, it is best to apply the capacitor bank just beyond the optimum loss-reduction location.

Batteries and capacitors seem similar as they both store and release electrical energy. However, there are crucial differences between them that impact their potential electronic applications due to how they function differently, depending on insulator material.

 

Supercapacitors

A capacitor battery aligns the molecules of a dielectric across an electric field to store energy. A supercapacitor aligns the charging of an electrolyte on either side of an insulator to store a double-layer charge.

Electrolytic capacitors consist of two or more conductive capacitors plate, separated by a dielectric. When an electric current enters the capacitor, the dielectric stops the flow and a charge builds up and is stored in an electric field between the metallic plates. Each capacitor is designed to have a particular capacitance (energy storage). When a capacitor is connected to an external circuit, a current will rapidly discharge. Plate area, separation, and dielectric constant together determine capacitance and thus energy density.

In a supercapacitor, there is no dielectric between conducting plates; rather, there is an electrolyte and a thin insulator such as cardboard or paper. When a current is introduced to the supercapacitor, ions build on either side of the insulator to generate a double layer of charge, no matter the capacitor charged. Supercapacitors are limited to low voltages, but very high capacitance frequencies, as a high voltage would break down the electrolyte. 

 

Batteries

There are different types of capacitor batteries, which detemine the capacitance of a capacitor. Different battery types are distinguished by their chemical makeup. The chemical unit, called the cell, contains three main parts; a positive terminal called the cathode, negative terminal called the anode, and the electrolyte. Batteries store electric energy. The battery charges and discharges through a chemical reaction that generates a voltage. The store of charge in the battery is able to provide a consistent DC voltage. In rechargeable batteries, the chemical energy that is converted into electricity can be reversed using an outside electrical energy to restore the charge of capacitors storing power in the batteries.

 

 

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Resistances in Parallel

Resistances in parallel share voltage, add conductances, and reduce equivalent resistance; apply Ohm's law, current division, and circuit analysis to compute total R, branch currents, and power distribution in multi-branch networks.

 

Resistances in Parallel Explained with Examples

Resistances in parallel is a common term used in industrial, commercial, and institutional power systems. Therefore, a good understanding of working with resistors in parallel and calculating their various parameters is crucial for maintaining safe and efficient operations. For foundational context, see this overview of electrical resistance for key definitions applied throughout.

It means that when resistors are connected in parallel, they share the same voltage across them. Hence, this means that the resistances are in parallel. This is because the total resistance of the resistors in parallel is less than that of any individual resistor, making it a useful configuration for reducing resistance and increasing current in a circuit. A clear grasp of electrical resistance helps explain why parallel branches draw more current.

Adding more resistors in parallel reduces the circuit's total resistance, increasing the current. However, adding too many resistors in parallel can overload the circuit and cause it to fail. Engineers often verify safe loading using the resistance formula to predict current increases.


Understanding Resistances in Parallel

They refer to the configuration in which two or more resistors are connected side by side across the same voltage points in an electrical circuit. In this arrangement, the voltage across each resistor is the same, while the current is divided among the resistors according to their resistance values. This configuration is commonly used in circuit analysis to simplify complex circuits and determine the equivalent parallel resistance.

When simplifying networks, computing the equivalent resistance streamlines analysis and component selection.


Calculating the Equivalent Resistance

To calculate the equivalent resistance of resistances in parallel, the reciprocal of the equivalent resistance (1/Req) is equal to the sum of the reciprocals of the individual resistances (1/R1 + 1/R2 + ... + 1/Rn). This formula is crucial in resistance calculation and helps engineers design efficient power systems that meet the desired voltage drop and current distribution requirements. A comparable reciprocal relationship appears when evaluating capacitance in series under similar analysis methods.

To calculate the total resistance of resistors in parallel, the reciprocal of each resistor is added together, and then the result is inverted to give the total resistance. This can be represented mathematically as:

1/Rt = 1/R1 + 1/R2 + 1/R3 + ...

where Rt is the total resistance and R1, R2, R3, etc. are the individual resistors.

 



Five resistors R(1) through R(5), connected in parallel, produce a net resistance R.

 

In a circuit with resistors in parallel, the current is divided among the resistors according to their individual resistance values. This is known as the current division, and it can be calculated using Ohm's law and the circuit's total resistance. The formula for calculating the current through each resistor in parallel is:

I1 = (V/R1) * (R2/(R2 + R3)) I2 = (V/R2) * (R1/(R1 + R3)) I3 = (V/R3) * (R1/(R1 + R2))

where I1, I2, and I3 are the currents through each resistor, V is the voltage across the circuit, and R1, R2, and R3 are the individual resistors.

Simplifying a circuit with resistors in parallel involves finding the equivalent resistance of the circuit. This is the resistance value that would produce the same current as the original parallel circuit, and it can be calculated using the reciprocal formula:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

where Req is the equivalent resistance.


Impact on Total Resistance

In a parallel configuration, adding more resistors decreases the total resistance. The reason is that the current has multiple paths to flow through, reducing the overall opposition to current flow. This characteristic is particularly useful in designing power supply systems, where lower resistance is desired to minimize energy losses and improve system efficiency. By contrast, capacitance in parallel increases as components are added, offering a helpful design analogy.


Practical Applications

They are employed in various real-life circuits and power systems. For instance, they are commonly found in circuit simulations, power distribution systems, and load balancing applications. In industrial settings, a parallel resistor calculator is often used to measure multiple current paths for fault protection and redundancy. In commercial and institutional power systems, parallel configurations are employed to manage load distribution and ensure system reliability.


Differences between Parallel and Series Connections

In a series circuit, resistors are connected end-to-end, and the current flows consecutively from the source of each resistor. The total resistance in a series circuit equals the sum of individual resistances, and the voltage drop across each single resistor is different. In contrast, they share the same voltage, and the total resistance decreases as more resistors are added. Identifying these connections in a circuit diagram is crucial for proper circuit analysis and design. For direct comparison of methods, review resistance in series to see how sums differ from reciprocals.


Combining Resistances in Parallel and Series

They can be combined with resistances in series within the same circuit. In such cases, equivalent resistances for both parallel and series sections are calculated separately. Then, the total resistance is determined by adding the equivalent resistances of the series and parallel sections. This approach helps engineers analyze complex circuits and design efficient power systems.

They are crucial to industrial, commercial, and institutional power systems. Understanding how to calculate the total resistance, current distribution, and power dissipation of resistors in parallel is essential for maintaining safe and efficient operations. In addition, engineers can optimize their designs for optimal performance by using circuit simulation software and other tools.

 

 

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