Electrical Resistance Explained

Capacitance in series reduces overall capacitance by summing the reciprocals of each capacitor. This concept is essential in electronics, circuit analysis, and power systems, ensuring proper charge storage, voltage division, and reliable circuit performance.

What is Capacitance in Series?

When capacitors are connected in series, their combined behavior follows specific rules that affect voltage distribution, total capacitance, and charge consistency.

✅ Reduces total capacitance as capacitors share the voltage

✅ Total capacitance is calculated using the reciprocal formula

✅ Charge on each capacitor is equal in a series circuit

In a series circuit, connecting more than one capacitor in series affects how voltage and charge are distributed, directly impacting the total capacitance of the system. Unlike parallel arrangements, a series setup reduces the overall capacitance and requires the use of a reciprocal formula to calculate the correct value. This configuration functions like a voltage divider, where the total voltage is split across each capacitor based on its individual capacitance. While this reduces the system’s ability to store charge, it also controls how voltage is allocated, which is useful in applications where precise energy storage and voltage regulation are needed.

For a clearer technical explanation, see our what is capacitance page, which breaks down how this key property affects circuit design.

When working with individual capacitors in electronic circuits, it is essential to understand their behaviour and effects. For example, in a series arrangement, the positive plate of one capacitor is connected to the negative plate of the next capacitor in line. This unique connection affects the circuit's total equivalent capacitance (C_total), resulting in a total capacitance that is smaller than the smallest individual capacitance (C) present in the series. The total capacitance of capacitors in series is always less than the value of the smallest individual capacitor in the arrangement.

A series circuit is characterized by its linear sequence of components, through which the current flows in a single path. In such circuits, the total voltage is distributed across each component in proportion to its resistance. The overall resistance of a series circuit is equal to the sum of the individual resistances of the connected components. The unit of capacitance, the farad, measures a capacitor’s ability to store electric charge per unit voltage.

When they are connected in series, the total C of the circuit is affected. This is because the positive plate of the capacitors is connected in series to the total C. Each capacitor stores the same charge in this arrangement, and the total voltage is divided across the capacitors in proportion to their C. This characteristic of series-connected capacitors plays a significant role in designing electronic circuits that require specific voltage and charge distribution properties. To fully grasp how capacitors behave in series, it’s important to understand what is a capacitor and how it stores and releases electrical energy.

Capacitors in Series: Formula, Voltage, and Charge Characteristics

Different types of capacitors, such as ceramic or electrolytic, behave differently in series configurations based on their construction and rated voltage.

Formula for Calculation

To accurately calculate the total C of capacitors connected in series, the following formula is employed:

C_total = 1 / (1/C1 + 1/C2 + 1/C3 + ... + 1/Cn)

This formula calculates the inverse of the total C. To find the actual total C, take the inverse of the sum of the inverse individual capacitances. This mathematical process enables the precise determination of the overall capacitance value in a series configuration, which is crucial when designing or analyzing electronic circuits.

Impact of the Smallest Capacitor on Total Capacitance

When several are connected in series, the total C becomes smaller than the smallest individual C. This phenomenon occurs because the capacitor with a smaller capacitance (C) limits the total capacitance (C), acting as a bottleneck for current flow and restricting the total charge stored in the circuit. Understanding this limiting effect is critical when selecting capacitors for a series configuration, as the smallest capacitor will significantly impact the overall performance of the electronic circuit. Engineers must also consider electrical resistance, which affects how current and voltage behave in conjunction with capacitors in mixed-component circuits.

Comparing Capacitors in Parallel and Series Configurations

In contrast to capacitors in series, when capacitors are connected in parallel, the total C is the sum of the individual capacitances. This difference occurs because each capacitor is directly connected to the power source in a parallel circuit, allowing it to store its charge independently. Consequently, capacitors in parallel configurations offer higher overall capacitance values, making them suitable for applications that require increased charge storage capabilities. Reviewing electrical resistance definition can help clarify how resistance and C work together in impedance-sensitive designs. You can explore how capacitance in parallel differs from series configurations when designing circuits requiring larger energy storage.

Equivalent Capacitance and Voltage Drop in Series Capacitors

The equivalent C of capacitors connected in series can be determined by dividing the total charge stored in the circuit by the total voltage across the circuit. This is because the total charge stored in the circuit equals the sum of the charges on each capacitor. In contrast, the total voltage is calculated to determine the total capacitance for the number of capacitors connected.

The voltage drop in capacitors connected in series is divided among the capacitors in proportion to their C. This means that the voltage across each capacitor is proportional to its C. Understanding the voltage drop distribution in series capacitors is essential when designing circuits that rely on specific voltage levels across components.

Replacing Capacitors in Series with a Single Equivalent Capacitor and Combination Circuits

In some cases, capacitors in series can be replaced with a single equivalent capacitor that has the same C value as the equivalent capacitance of the series capacitors. This replacement technique can simplify circuit design and analysis, consolidating multiple components into a single element with equivalent electrical properties.

In a combination circuit, capacitors are connected in both series and parallel configurations. These complex arrangements are commonly found in practical electronic applications, as they offer more flexibility and adaptability in achieving desired circuit properties. To calculate the total C of a combination circuit, first, compute the capacitance of each series combination, then add those capacitances to find the total C. This process may involve several steps, as the designer needs to consider the contributions of both series and parallel components to the overall C value.

Applications and Considerations of Capacitors in Series

Capacitors in series configurations are utilized in various electronic applications, such as power supply filtering, signal coupling, and decoupling, as well as in tuning and timing circuits. When designing these applications, engineers must consider the capacitors' voltage ratings, tolerances, temperature coefficients, and other parameters to ensure the circuit functions as desired.

One crucial consideration when working with capacitors in series is the voltage rating. The voltage rating of each capacitor must be sufficient to handle the voltage that will be applied across it. Since the total voltage is distributed among the capacitors in series, selecting capacitors with appropriate voltage ratings is essential to prevent component failure or degradation.

Another important consideration is the capacitors' tolerances, which indicate the possible variation in C values from their nominal specifications. Capacitors with tighter tolerances may be required for precise applications, as variations in C values can impact the overall performance of the electronic circuit. 

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Electricity supply covers generation, transmission, distribution, grid infrastructure, voltage regulation, frequency control, power quality, protection, SCADA, and load management to ensure reliable energy delivery to industrial, commercial, and residential loads.

What Is Electricity Supply?

Electricity supply is generation, transmission and distribution of power with set voltage, frequency and reliability.

✅ Involves generation, HV transmission, MV/LV distribution networks

✅ Ensures voltage regulation, frequency control, and power quality

✅ Uses SCADA, protection relays, and load forecasting for reliability

What Is Electricity Supply?

Electricity Supply is a complex balanced system of electric power generation and real time customer demand. Production (supply) and consumption (demand) dictate electricity pricing in the United States and Canada.  For a regional view, the analysis at Electricity Demand in Canada highlights how seasonal peaks and resource availability shape prices.

Where does the term "electricity supply" originate? How does that supply move from one point to another? These are most important questions to ask when you want to understand the electric power industry.

If you're new to the vocabulary, the concise glossary at Electricity Terms can clarify definitions used throughout the industry.

The first thing to know is that electric power is generated in the United States and Canada in power plants which house electrical generators. Then, power is transported (transmission and distriubtution) through the power grid to the customer. This complex network of transmission lines delivers power to industrial, commercial, institutional and residential customers. For a step-by-step overview of system operations, Electricity: How It Works explains generation, transmission, and distribution in practical detail.

In the electricity industry, transmission and distribution wires do the work of transporting power to satisfy electricity demand during real time peak demand. This is the job of the electricity market. The natural gas and fossil fuels industry works in the same way. These lines run from generating station to substations (sometimes over great distances, like in the case of British Columbia and Manitoba where generation is in the far north and the consumption is in the south. This is where the voltage is reduced for local consumption. Substations are usually located close to where the electricity is consumed. 

For background on core power concepts, the primer at Electricity Power connects voltage, current, and load to real-world grid behavior.

The various prices of electricity depends on the electricity supply mix and the energy efficiency of the customer. Electricity energy supply is usually measured in terawatt hours.

The system design is of three-phase alternating current electrical generation and distribution, which was invented by Nikola Tesla in the 19th century. He considered that 60 Hz was the best frequency for alternating current (AC) power generating Electricity Supply. He preferred 240 V, which was claimed to be better for long supply lines. Thomas Edison developed direct current (DC) systems at 110 V and this was claimed to be safer. For more information about the early battles between proponents of AC and DC supply systems see War of Currents. For foundational fundamentals beyond this history, the overview at What Is Electricity clarifies the principles common to both AC and DC systems.

The German company AEG built the first European generating facility to run at 50 Hz, allegedly because the number 60 did not fit into the numerical unit sequence of 1, 2, 5…. At that time, AEG had a virtual monopoly and their standard spread to the rest of the continent. In Britain, differing frequencies (including 25 Hz 40 Hz and DC) proliferated, and the 50 Hz standard was established only after World War II.

To see how frequency standards interact with generation and end-use performance, the explainer at How Electricity Works ties design choices to everyday operation.

Originally much of Europe was 110 V too, just like the Japanese and the US system today. It was deemed necessary to increase the necessary voltage to draw more electrical power with reduced energy loss and voltage drop from the same copper wire diameter.

The choice of utilization voltage is governed more by tradition than by optimization of the distribution system. In theory, a 240 V distribution system will use less conductor material to deliver a given quantity of power. Incandescent lamps for 120 V systems are more efficient and rugged than 240 V lamps, while large heating appliances can use smaller conductors at 240 V for the same output rating. Practically speaking, few household appliances use anything like the full capacity of the outlet to which they are connected. Minimum wire sizes for hand-held or portable equipment is usually restricted by the mechanical strength of the conductors. One may observe that both 240 V system countries and 120 V system countries have extensive penetration of electrical appliances in homes. National electrical codes prescribe wiring methods intended to minimize the risk of electric shock or fire. For household applications, home electricity basics show how these voltage considerations affect outlets, circuits, and safety practices.

Areas using (approximately) 120V allow different combinations of voltage, suitable for use by a variety of classes of electrical equipment.

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Current is the flow of electric charge in circuits, defined by amperage, driven by voltage, limited by resistance, described by Ohm’s law, and fundamental to AC/DC power systems, loads, conductors, and electronic components.

What Is Current?

Current is charge flow in a circuit, measured in amperes and governed by voltage and resistance.

✅ Measured in amperes; sensed with ammeters and shunts

✅ Defined by Ohm’s law: I = V/R in linear resistive circuits

✅ AC alternates; DC is steady; sets power transfer P = V*I

Current is best described as a flow of charge or that the charge is moving. Electrons in motion make up an electric current. This electric current is usually referred to as “current” or “current flow,” no matter how many electrons are moving. Current is a measurement of a rate at which a charge flows through some region of space or a conductor. The moving charges are the free electrons found in conductors, such as copper, silver, aluminum, and gold. The term “free electron” describes a condition in some atoms where the outer electrons are loosely bound to their parent atom. These loosely bound electrons can be easily motivated to move in a given direction when an external source, such as a battery, is applied to the circuit. These electrons are attracted to the positive terminal of the battery, while the negative terminal is the source of the electrons. The greater amount of charge moving through the conductor in a given amount of time translates into a current. For a concise overview of how moving charges create practical circuits, see this guide to current electricity for additional context.

The System International unit for current is the Ampere (A), where

That is, 1 ampere (A) of current is equivalent to 1 coulomb (C) of charge passing through a conductor in 1 second(s). One coulomb of charge equals 6.28 billion billion electrons. The symbol used to indicate current in formulas or on schematics is the capital letter “I.” To explore the formal definition, standards, and measurement practices, consult this explanation of the ampere for deeper detail.

When current flow is one direction, it is called direct current (DC). Later in the text, we will discuss the form of current that periodically oscillates back and forth within the circuit. The present discussion will only be concerned with the use of direct current. If you are working with batteries or electronic devices, you will encounter direct current (DC) in most basic circuits.

The velocity of the charge is actually an average velocity and is called drift velocity. To understand the idea of drift velocity, think of a conductor in which the charge carriers are free electrons. These electrons are always in a state of random motion similar to that of gas molecules. When a voltage is applied across the conductor, an electromotive force creates an electric field within the conductor and a current is established. The electrons do not move in a straight direction but undergo repeated collisions with other nearby atoms. These collisions usually knock other free electrons from their atoms, and these electrons move on toward the positive end of the conductor with an average velocity called the drift velocity, which is relatively a slow speed. To understand the nearly instantaneous speed of the effect of the current, it is helpful to visualize a long tube filled with steel balls as shown in Figure 10-37. It can be seen that a ball introduced in one end of the tube, which represents the conductor, will immediately cause a ball to be emitted at the opposite end of the tube. Thus, electric current can be viewed as instantaneous, even though it is the result of a relatively slow drift of electrons. For foundational concepts that connect drift velocity with circuit behavior, review this basic electricity primer to reinforce the fundamentals.

Current is also a physical quantity that can be measured and expressed numerically in amperes. Electric current can be compared to the flow of water in a pipe. It is measureda at the rate in which a charge flows past a certain point on a circuit. Current in a circuit can be measured if the quantity of charge "Q" passing through a cross section of a wire in a time "t" (time) can be measured. The current is simply the ratio of the quantity of charge and time. Understanding current and charge flow also clarifies how circuits deliver electrical energy to perform useful work.

Electrical current is essentially an electric charge in motion. It can take either the form of a sudden discharge of static electricity, such as a lightning bolt or a spark between your finger and a ground light switch plate. More commonly, though, when we speak of current, we mean the more controlled form of electricity from generators, batteries, solar cells or fuel cells.  A helpful overview of static, current, and related phenomena is available in this summary of electricity types for quick reference.

We can think of the flow of electrons in a wire as the flow of water in a pipe, except in this case, the pipe of water is always full. If the valve on the pipe is opened at one end to let water into the pipe, one doesn't have to wait for that water to make its way all the way to the other end of the pipe. We get water out the other end almost instantaneously because the incoming water pushes the water that's already in the pipe toward the end. This is what happens in the case of electrical current in a wire. The conduction electrons are already present in the wire; we just need to start pushing electrons in one end, and they start flowing at the other end instantly. In household power systems, that push on conduction electrons alternates in direction as alternating current (AC) drives the flow with a time-varying voltage.

Current Formula

Current is rate of flow of negatively-charged particles, called electrons, through a predetermined cross-sectional area in a conductor.

 Essentially, flow of electrons in an electric circuit leads to the establishment of current.

q = relatively charged electrons (C)

t = Time

Amp = C/sec

Often measured in milliamps, mA

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Generate electricity via power generation methods: generators, turbines, photovoltaics, fuel cells, and microgrids; optimized by inverters, AC/DC conversion, smart grid control, energy storage, high-efficiency transmission, and reliable distribution networks integration.

What Is Generate Electricity?

Generate electricity converts energy to electric power using generators, turbines, and inverters for grid supply.

✅ Electromechanical conversion with synchronous or induction generators

✅ Power electronics: rectifiers, inverters, MPPT, AC/DC conversion

✅ Sources: PV, wind, hydro, gas turbines; grid-tied or microgrid

There are several ways to generate electricity. There are "thermal" methods like coal, oil, natural gas, peat, biomass - in all these cases, the energy that is trapped in the form of carbon (found in the ground in the form of fossil fuels) is released by heating the carbon. The problem, as we all know too well, is that the breakdown of carbon through burning it is the by product of gases such as carbon dioxide, a main contributor to global warming. But that is not all. When we burn carbon, there are other pollutants that are released into the atmosphere like sulphur dioxide and nitrous oxide. These chemicals are the principal contributors to acid rain. For a broader overview of these processes, see how electricity generation works across different fuel types.

We also produce electricity by non-fossil fuel methods by using uranium in nuclear fission "reactors" to create enough heat to boil water, which in turn produces large quantities of high pressure steam. This steam turns a turbine which turns a generator that manufactuers electic power through the conversion of mechanical energy into electrical energy. This sequence illustrates how electricity is generated from thermal sources in practice.

There is more than one renewable source of energy to generate electricity, by using solar panels to convert sunlight and wind energy to convert kinetic energy into electric power. In any case dependable power generation, transmission and distribution is critical for providing heat, light and power for human activities. Electric power has been generated for the purpose of powering human technologies for at least 120 years from various sources of potential energy. The first power plants were run on wood, while today we rely mainly on oil, natural gas, coal, hydroelectric and nuclear power and a small amount from hydrogen, solar energy, tidal harnesses, wind generators, and geothermal sources. Many utilities are expanding portfolios with alternative electricity options to meet emissions targets.

Methods To Produce Electric Power

Understanding the landscape of sources of electricity helps frame the methods described below.

Rotating turbines attached to electrical generators produce most commercially available electricity. Turbines may be driven by using steam, water, wind or other fluids as an intermediate energy carrier. The most common usage is by steam in fossil fuel power plants or nuclear power plants, and by water in hydroelectric dams. Alternately, turbines can be driven directly by the combustion of natural gas or oil. Combined cycle gas turbine plants offer efficiencies of up to 60%. They generate power by burning natural gas in a gas turbine and use residual heat to generate additional electric power from steam. Wind turbines create power by using the wind. Solar updraft towers use wind that is artificially produced inside the chimney by heating it with sunlight. Solar parabolic troughs and solar power towers concentrate sunlight to heat a heat transfer fluid that is used to produce steam to turn a turbine. In all these configurations, the core electricity generator converts rotational energy into electrical output.

Within wind applications, the modern electricity windmill integrates power electronics and control systems to maximize capacity factor.

Small power generators are often powered by reciprocating engines burning diesel, biogas or natural gas. Diesel engines are often used to create power, usually at low voltages. Biogas is often combusted where it is produced, such as a landfill or wastewater treatment plant, with a reciprocating engine or a microturbine, which is a small gas turbine. These distributed assets play a growing role in overall electricity production for remote sites and microgrids.

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The Ohm's Law formula is a cornerstone of electrical engineering, serving as a basis for analyzing and designing electric circuits. Its applications range from determining the appropriate values of electrical components to predicting the behaviour of complex systems. By exploring the relationship between voltage, current, and resistance and their connections with other fundamental laws in electromagnetism, we can gain a deeper understanding of the principles that govern the flow of electricity and its conversion into other forms of energy.

Ohm's Law states that the relationship between voltage, current, and resistance. This law, named after its discoverer Georg Simon Ohm, has wide-ranging applications in various fields, from the design of simple electrical circuits to complex electronic systems.

Ohm's Law, denoted as V=IR, dictates that the voltage (V) across a conductor between two points is directly proportional to the current (I) flowing through it, as long as the resistance (R) of the material remains constant. This equation lays the foundation for understanding electric circuits, and its relevance extends to both alternating current (AC) and direct current (DC) systems.

Let's consider a simple scenario to implement Ohm's Law. In an electrical circuit, a battery supplies voltage (also called electric potential or electromotive force), which causes electrons to flow, generating an electric current. The flow of these electrons encounters resistance due to the physical properties of the materials used in the circuit. The higher the resistance, the more the material opposes the flow of electrons, leading to a decrease in the electric current.

A practical application of Ohm's Law calculator can be found in determining a resistor's suitable value for a circuit. Using the formula V=IR, you can calculate the required resistance by rearranging the equation as R=V/I, where you substitute the known voltage and current values to find the unknown resistance.

When it comes to units, voltage is measured in volts (V), current in amperes (A), and resistance in ohms (Ω). It is essential to be mindful of these units when working with electrical components, as they determine the overall performance and safety of the system.

While Ohm's Law plays a critical role in understanding electric circuits, it is also interconnected with the concept of conductivity. Conductivity, a measure of a material's ability to conduct electrical energy, is the reciprocal of resistance. The more conductive a material is, the less resistance it exhibits, and vice versa. Conductivity helps engineers and designers select the right materials for specific applications, ensuring the efficiency and reliability of electrical systems.

However, Ohm's Law has its limitations. In real-world scenarios, resistance may not remain constant for all materials and under all conditions. Factors such as temperature, pressure, and the material's non-linear behaviour can cause deviations from the ideal behaviour predicted by Ohm's Law. As a result, this law is considered an ideal approximation for most practical purposes but may not be universally applicable.

Ohm's Law is also related to other fundamental laws in electromagnetism, such as Faraday's, Lenz's, and Biot-Savart's law. Faraday's Law describes the induction of voltage in a conductor moving through a magnetic field, while Lenz's Law explains the direction of the induced current due to this magnetic field. The Biot-Savart Law, on the other hand, calculates the magnetic field generated by an electric current. Understanding these laws is vital for grasping more complex concepts and phenomena in electromagnetism and their practical applications.

How to use Ohm's Law Equation

Let's consider an example of how to use Ohm's Law in a practical situation.

Suppose you have a 12-volt (V) battery connected to a simple electrical circuit with a single resistor. The current flowing through the resistor is measured to be 2 amperes (A). You can use Ohm's Law to calculate the resistance of the resistor in the circuit.

Recall the Ohm's Law formula: V = IR, where V is voltage, I is current, and R is resistance.

In this example, we know the voltage (V = 12 V) and the current (I = 2 A), and we want to find the resistance (R).

Rearrange the formula to solve for resistance: R = V / I

Now, substitute the known values into the formula:

R = 12 V / 2 A

R = 6 ohms (Ω)

So, the resistance of the resistor in this circuit is 6 ohms. By using Ohm's Law, you can determine unknown values in a circuit, such as resistance, as long as you have the other two known values (voltage and current).