Resistance Formula Explained

Electrical energy is the power derived from the movement of electrons through a conductor. It powers homes, industries, and modern technology. This form of energy can be generated from various sources, including fossil fuels, solar, wind, and hydroelectric systems.

What is Electrical Energy?

Electrical energy is the result of electric charge flow, used to perform work in countless applications across daily life and industry.

✅ Powers lighting, heating, and electronic devices across all sectors

✅ Generated by power plants from renewable and non-renewable sources

✅ Converted from and into other energy forms, like mechanical or thermal

Electrical Energy: The Fundamental Source of Power

An Electric charge is a property of certain subatomic particles (e.g., electrons and protons) which interacts with the electromagnetic field and causes attractive and repulsive forces between them. Electric charges give rise to one of the four fundamental forces of nature, and is a conserved property of matter that can be quantified. In this sense, the phrase "quantity of electricity" is used interchangeably with the phrases "charge of electricity" and "quantity of charge." There are two types of charge: we call one kind of charge positive and the other negative. Through experimentation, we find that like-charged objects repel and opposite-charged objects attract one another. Coulomb's law gives the magnitude of the force of attraction or repulsion. For a broader understanding, visit how electricity works to see how it is generated, transmitted, and used across power grids and homes.

How Electric Fields Transfer Energy Between Charges

Michael Faraday introduced the concept of the Electrical Energy field. The field force acts between two charges, in the same way that the gravitational field force acts between two masses. However, the electric field is a little bit different. Gravitational force depends on the masses of two bodies, whereas the electromagnetic force depends on the electric charges of two bodies. While gravity can only pull two masses together, the force can be attractive or repulsive. If both charges are of the same sign (e.g. both positive), there will be a repulsive force between the two. If the charges are opposite, an attractive force will exist between the two bodies (as seen in static electricity and kinetic energy). The magnitude of the force varies inversely with the square of the distance between the two bodies and is also proportional to the product of the unsigned magnitudes of the two charges. Discover how electrical load determines the demand placed on a system’s energy supply.

Electrical Energy and Voltage Explained

The electric potential difference between two points is defined as the work done per unit charge (against forces) in moving a positive point charge slowly from one point to another. Choose one point as a reference with zero potential. The electric potential at any other point equals the work required per unit charge to move a positive test charge from the reference point to that location. For isolated charges, the reference point is usually taken to be infinity. The potential is measured in volts. (1 volt = 1 joule/coulomb) The electric potential is analogous to temperature: there is a different potential at every point in space, and the potential gradient indicates the direction and magnitude of the driving force behind electric current flow. Similarly, there is an electric potential at every point in space, and its gradient indicates the direction and magnitude of the driving force behind the movement of charged energy. To understand how voltage influences electrical energy, it's essential to grasp how potential difference drives current through circuits.

Electric Current: Flow of Charge That Powers Technology

Current is a flow of electrical energy, and its intensity is measured in amperes. Examples of electric currents include metallic conduction, where electrons flow through a conductor such as a metal wire, and electrolysis, where ions (charged atoms) flow through liquids. The particles themselves often have energy to move quite slowly, while the moving electric field that drives them propagates at close to the speed of light. See energy conduction for more information. Alternating current and direct current each transfer electrical energy differently, depending on the application.

Devices that utilize charge flow principles in materials are referred to as electronic devices.

A direct current (DC) is a unidirectional flow, while an alternating current (AC) reverses direction repeatedly. The time average of an alternating current is zero, but its capability (RMS value) is not zero.

Ohm's Law is an important relationship describing the behaviour of energy, relating it to voltage. Explore the principles behind Ohm’s Law to see how voltage, current, and resistance interrelate in determining energy flow. Learn how electrical resistance affects energy loss and heat generation in systems.

For historical reasons, power is said to flow from the most positive part of a circuit to the most negative part. The current thus defined is referred to as conventional current. It is now known that, depending on the conditions, a current can consist of a flow of charged particles in either direction, or even in both directions at once. The positive-to-negative convention is widely used to simplify this situation. If another definition is used - for example, "electron current" - it should be explicitly stated.

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Equivalent resistance is the total resistance of a circuit that simplifies multiple resistors into a single resistor. It is calculated differently for series and parallel circuits, helping determine current flow, voltage distribution, and overall power consumption in electrical networks.

What is Equivalent Resistance?

Equivalent resistance is a crucial concept for individuals working with electrical circuits. It: 

✅ Represents the single resistance that replaces multiple resistors in a circuit.

✅ Simplifies calculations of current, voltage, and power.

✅ Found using series or parallel formulas based on resistor arrangement.

By mastering the calculation methods for series and parallel circuits, understanding the relationship with Ohm's law, and applying Kirchhoff's laws in more complex situations, you can efficiently analyze and design electrical systems that meet the requirements of various applications. Furthermore, by incorporating equivalent resistance calculations into your skillset, you'll be better prepared to tackle the exciting challenges presented by the ever-evolving world of electronics and power systems.

Equivalent Resistance in Series vs. Parallel Circuits

To calculate the equivalent resistance of a network, it is often necessary to determine the sum of the individual resistances. This involves adding the resistance values of each individual resistor in the network, providing a baseline for further calculations. This is a resistance formula for a single resistor, as well as for calculating resistors connected in parallel or in series.

Electrical resistance (R) is a measure of the opposition to the flow of electric current within a circuit. It is determined by the material and dimensions of the conductor, as well as the temperature and other environmental factors. It is measured in ohms (Ω), with lower R indicating greater conductivity and vice versa.

Equivalent Resistance Formula

When a group of resistors is connected end-to-end, they form a series. In a series circuit, the total resistance is equal to the sum of the individual Rs, as current must flow through each resistor in turn. The equivalent resistance of a series circuit is calculated by adding the values of each individual resistor:

Req = R1 + R2 + R3 + ...

Resistors connected across the same potential difference, or applied voltage, are referred to as being connected in parallel. In a parallel circuit, the total R is less than the R of any individual resistor as the current divides among the resistors. The equivalent resistance of a parallel circuit is calculated using the reciprocal formula:

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

Equivalent resistance is the single R value that can replace a group of resistors in a circuit, offering the same overall R. This simplifies circuit analysis and allows for more straightforward calculations of current and voltage values.

Ohm's law is an essential principle in electronics and relates closely to equivalent resistance. Ohm's law states that the current (I) flowing through a resistor is directly proportional to the applied voltage (V) and inversely proportional to the R. The equation is:

V = IR

By calculating equivalent resistance for a given circuit, we can use Ohm's law to determine the overall current flowing through the circuit and the voltage drops across each resistor.

Series and parallel circuits exhibit different properties when it comes to equivalent resistance. In series circuits, the overall R increases with the addition of more resistors, which means the total current will decrease. In parallel circuits, adding more resistors results in a decrease in total resistance, causing an increase in total current. Understanding these differences is crucial for designing circuits that meet specific electrical requirements.

Kirchhoff's Law

Kirchhoff's laws are another essential tool for calculating equivalent resistance in more complex circuits that cannot be simplified as purely series or parallel. Kirchhoff's current law (KCL) states that the sum of currents entering a junction in a circuit must equal the sum of currents leaving the junction. Kirchhoff's voltage law (KVL) asserts that the sum of the voltages around any closed loop in a circuit must equal zero. By applying these laws, we can create a system of equations to solve for unknown resistance values in a network, ultimately determining the equivalent resistance.

Real-World Applications

Real-world applications of equivalent resistance can be found in various fields, such as electronics, power distribution, and telecommunications. For example, various components have different R values in electronic devices, such as smartphones. Calculating the equivalent resistance enables engineers to design efficient power management systems, ensuring optimal performance and extended battery life. In power distribution networks, equivalent resistance calculations are essential for determining voltage drops and current values across transmission lines, enabling the design of efficient and reliable power delivery systems.

Understanding equivalent resistance is vital for professionals and students who deal with electrical circuits. From simplifying complex networks to designing efficient circuits, equivalent resistance plays a central role in analyzing and developing modern electronic systems. Familiarity with this concept and associated principles like Ohm's law and Kirchhoff's laws ensures a strong foundation for anyone working with electronics, power systems, and telecommunications.

Technology Advances

As technology advances, the importance of equivalent resistance in designing and analyzing new devices and systems will only grow. Calculating and understanding equivalent resistance enables engineers to push the boundaries of innovation and improve upon existing systems, resulting in more efficient, high-performance solutions for consumers and industries alike.

To further develop your understanding of equivalent resistance and related concepts, consider exploring the wealth of educational resources available online and in textbooks, as well as seeking hands-on experience through workshops or real-world projects. Applying this knowledge to practical scenarios will enable you to tackle various electrical and electronic challenges.

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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. 

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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Electricity demand Canada drives load forecasting, grid reliability, peak demand management, renewable integration, and capacity planning across provinces, informing energy consumption trends, transmission constraints, demand response programs, and ISO market operations.

What Is Electricity Demand Canada?

It is the national electrical load across sectors guiding forecasting, grid planning, and reliability.

✅ Provincial load profiles and peak diversity analysis

✅ Demand response and time-of-use optimizing peak loads

✅ Transmission constraints and capacity expansion planning

Electricity Demand in Canada will continue to put, in the longer term, upward pressure on prices for consumers in both regulated and restructured or deregulated markets. For context, market fundamentals and policy design both shape electricity prices across provinces today, influencing bills over time.

These dynamics play out within an integrated electric power system that balances reliability, affordability, and decarbonization goals.

These pricing impacts will be felt due to the cost of developing new generation and transmission facilities in order to replace ageing infrastructure and due to the increased use of renewable sources of generation (e.g., wind, solar, biomass). Continued strength of oil and gas prices are expected to keep electricity prices higher in regions that rely on natural gas and oil products as input fuels for power generation. Understanding the mix of hydro, wind, solar, nuclear, and gas requires a grasp of how electricity is generated across Canada’s grid components.

With the exception of Ontario (due to its large summer seasonal air conditioning requirement for electricity demand, Canada is a winter-peaking system and so the highest demand loads usually occur in the winter. However, for provinces that have competitive wholesale markets (e.g. Alberta and Ontario), near-term price pressures could result from the increase in summer cooling demand. Prices could also experience additional upward pressure from fuels used to generate electricity; namely, oil and natural gas. These pressures could be further supported by unusual weather events, unplanned generation outages and transmission system failures. If wholesale price pressures are to be passed on to consumers, the cost impact would likely not be felt immediately. Instead, such costs would need to go through a review process in all provinces and be approved by the energy regulatory board of that respective province. Tight reserve margins can constrain electricity supply during extreme temperature events, amplifying short-term price volatility.

Consumer prices or "rates" vary for several reasons:

In many jurisdictions, the total electricity cost combines generation, transmission, distribution, and rider charges that appear separately on bills.

• variation in generation costs; prices in hydro-based provinces tend to be lower (e.g., British Columbia, Manitoba and Quebec);
• customer class (e.g., residential, commercial, industrial);
• residential rates tend to be higher than commercial and industrial rates;
• amount of energy consumed in a given period (e.g., rates may vary based on customer consumption);
• time-of-use pricing (e.g., some consumers have access to time of use meters that show lower charges for electricity during off peak periods);
• and capability to switch to lower cost fuels (e.g. industrial customers)

Consumers in deregulated provinces can compare plans from an electricity supplier to align contract terms and risk with their usage profile.

Electricity demand Canada in peak periods typically occurs during the winter months, although, at times, Ontario and Quebec experience peak electricity demand in the summer months due to increased use of air conditioning units. Spring and fall tend to be shoulder seasons with lower demand. Seasonal patterns also influence maintenance schedules for electricity generation across provinces, which can tighten supply during cold snaps or heat waves.

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Harmonic distortion is the deviation from the ideal electrical waveform caused by nonlinear loads. It impacts power quality, increases heat in equipment, and can lead to system inefficiencies. Monitoring and mitigation are essential in industrial electrical systems.

What is Harmonic Distortion?

Harmonic distortion is not a new phenomenon in power systems. Concern over distortion has fluctuated several times throughout the history of AC electric power systems.

✅ Reduces overall power quality and system reliability

✅ Can damage equipment and increase heat generation

✅ Requires monitoring to ensure system efficiency and safety

In the 1930s and 1940s, the primary sources were transformers, with the primary problem being inductive interference with open-wire telephone systems. Early arc lighting caused similar concern due to its harmonic content, just as today’s electronic power converters do.

Today, nonlinear devices like variable frequency drives (VFDs), arc furnaces, computer power supplies, and LED lighting introduce significant harmonic distortion into electrical systems. Nonlinear devices do not draw current in a linear relationship to voltage, which distorts the sinusoidal waveform and introduces harmonic currents. Harmonic distortion is one of the many issues covered in our comprehensive Power Quality resource channel, which explores causes, effects, and solutions.

Why It Matters

• Harmonics degrade power quality

• Increase energy losses and heat in conductors and transformers

• Lead to premature failure of motors and sensitive electronics

• Interfere with communication lines

In contrast, voltage sags and interruptions are nearly universal to every feeder and represent the most numerous and significant power quality deviations. The end-user sector suffers more from harmonic problems than the utility sector. Industrial users with adjustable speed drives, arc furnaces, induction furnaces, and similar equipment are significantly more susceptible to problems caused by harmonic distortion. To understand the relationship between harmonics and apparent energy flow, see our explanation of Apparent Power vs Real Power.

A good assumption for most utilities in the United States is that the sine wave voltage generated in central power stations is very good. In most areas, the voltage found on transmission systems typically has much less than 1% distortion. However, the distortion increases as the load approaches. At some loads, the current waveforms barely resemble a sine wave. Electronic power converters can chop the current into seemingly arbitrary waveforms. Managing nonlinear loads often requires Power Factor Correction to reduce harmonic effects and improve efficiency.

Industry Standards

• IEEE 519: Sets recommended harmonic limits for both voltage and current.

• IEC 61000-4-7: Defines methods of measuring harmonics and interharmonics.

Harmonic Distortion and Nonlinear Devices

Harmonic distortion is caused by nonlinear devices in the power system. A nonlinear device is one in which the current is not proportional to the applied voltage. Figure 1 illustrates this concept using the case of a sinusoidal voltage applied to a simple nonlinear resistor, where the voltage and current vary according to the curve shown. While the applied voltage is perfectly sinusoidal, the resulting current is distorted. Increasing the voltage by a few percent may cause the current to double and exhibit a different waveform. You can calculate your system’s power quality impact using our Apparent Power Calculator for precise performance metrics.

This is the source of most harmonic distortion in a power system. Figure 1 illustrates that any periodic, distorted waveform can be expressed as a sum of sinusoids. When a waveform is ideal from one cycle to the next, it can be represented as a sum of pure sine waves in which the frequency of each sinusoid is an integer multiple of the fundamental frequency of the distorted wave. This multiple is called a harmonic of the fundamental, hence the name of this subject matter. The sum of sinusoids is referred to as a Fourier series, named after the great mathematician who discovered the concept. Nonlinear loads like VFDs and arc furnaces can affect grounding; learn more in our guide to Electrical Grounding.

Fig. 1. Current distortion caused by nonlinear resistance

Voltage and Current Distortion

The term "harmonics" is often used by itself without further qualification. Generally, it could mean one of the following three:

1. The harmonic voltages are too great (the voltage is too distorted) for the control to properly determine firing angles.

2. The harmonic currents are too great for the capacity of some devices in the power supply system, such as transformers, and the machine must be operated at a lower than rated power.

3. The harmonic voltages are too great because the harmonic currents produced by the device are too great for the given system condition.

Clearly, there are separate causes and effects for voltages and currents, as well as some relationship between them. Thus, the term harmonics by itself is inadequate to describe a problem definitively. Nonlinear loads appear to be sources of harmonic current, injecting harmonic currents into the power system. For nearly all analyses, it is sufficient to treat these harmonic-producing loads simply as current sources. There are exceptions to this as described later.

Fig 2. Harmonic currents flowing through the system impedance result in harmonic voltages at the load.

Voltage distortion is the result of distorted currents passing through the linear, series impedance of the power delivery system, as illustrated in Fig. 2. Although assuming that the source bus is ultimately a pure sinusoid, there is a nonlinear load that draws a distorted current. The harmonic currents passing through the system's impedance cause a voltage drop for each harmonic. This results in voltage harmonics appearing at the load bus. The amount of voltage distortion depends on the impedance and the current. Assuming the load bus distortion stays within reasonable limits (e.g., less than 5%), the amount of harmonic current produced by the load is generally constant.

While the load current harmonics ultimately cause voltage distortion, it is worth noting that the load has no control over the voltage distortion. The same load put in two different locations on the power system will result in two different voltage distortion values. Recognition of this fact is the basis for the division of responsibilities for harmonic control that is found in standards such as IEEE Std 519-1992.

• Control over the amount of harmonic current injected into the system occurs at the end-use application.

• Assuming the harmonic current injection is within reasonable limits, the control over voltage distortion is exercised by the entity that controls the system impedance, typically the utility.

One must be careful when describing harmonic distortion phenomena, as there are distinct differences between the causes and effects of harmonic voltages and currents. The use of the term harmonics should be qualified accordingly. By popular convention in the power industry, the term is used by itself most of the time when referring to load apparatus, indicating that the speaker is referring to the harmonic currents. When referring to the utility system, the voltages are generally the subject. For systems affected by harmonic-induced overheating, understanding Capacitor Bank applications is essential for voltage support and harmonic filtering. For in-depth harmonic analysis, explore our guide to using a Power Quality Analyzer to identify waveform distortion and power anomalies.

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Home electricity powers lighting, appliances, and electronics using energy from the grid or renewable sources like solar. Understanding usage, safety, and efficiency helps reduce costs and improve performance in daily life.

What is Home Electricity?

Home electricity refers to the power used to operate household systems and devices.

✅ Powers lights, appliances, HVAC, and electronics

✅ Supplied by utilities or solar energy systems

✅ Measured in kilowatt-hours and billed monthly

How Electricity Enters and Flows Through Your Home

Electricity originates from a distant power station, fueled by coal, natural gas, nuclear power, or renewable sources, and is transformed into high-voltage energy for long-distance transmission. Along the way, transformers step this voltage down to safe, usable levels. When it reaches your home, the electricity flows through a service line to a main panel, where circuit breakers distribute it to branch circuits that power every room and outlet.

In the United States, most residential circuits provide about 120 volts of alternating current (AC) at 60 Hz. Voltage measures the energy per unit charge: 120 volts means 120 joules of energy are transported by each coulomb of charge. One coulomb per second equals one ampere, so an appliance drawing 1 ampere at 120 volts consumes energy at 120 watts—120 joules per second.

How Appliances Use Electrical Energy

When you switch on an appliance, it allows 120 volts of potential to push current through the device—similar to using water pressure to move water through a pipe. As electric charge flows, energy is transformed into useful work like heating, lighting, or mechanical motion. Voltage gradually drops to nearly zero by the time the current exits the appliance.

This “spent” charge is carried back to your electrical panel via the neutral wire and ultimately to the ground through the grounding system. The ground serves as a vast reservoir, stabilizing voltages and protecting users in the event of a fault.

Understanding Home Wiring and Safety

In a standard polarized receptacle, the smaller prong connects to the hot wire (120 volts), and the wider prong to the neutral (0 volts). The hot wire delivers the current; the neutral completes the circuit back to the panel. A separate ground wire exists for safety—it’s not part of the working circuit but protects against electric shock if a fault occurs.

Most wall outlets contain two receptacles (a duplex) wired in parallel. This means two appliances plugged in will receive the same 120-volt supply but can draw different amounts of current. Parallel wiring is standard throughout the home, allowing consistent voltage distribution while accommodating various electrical loads.

Where the Energy Comes From and Where It Goes

Electricity used at home ultimately comes from generators that elevate the voltage of electric charge before it travels across the grid. After powering your home, the now low-energy charge returns to the ground. This closed-loop system—from the earth to the generator and back—enables efficient energy use and the safe disposal of spent charge.

Whether your electricity comes from traditional utilities or rooftop solar panels, the underlying principles remain the same: raise voltage at the source, deliver it efficiently, use it safely, and return it to ground. Understanding these concepts helps homeowners stay informed, reduce waste, and use electricity more safely and effectively.

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