Wireless Electricity

The voltage drop formula is V = I × R, where V represents the voltage drop, I represents the current in amperes, and R represents the resistance in ohms. It calculates the amount of voltage lost through a conductor and is essential for designing safe and efficient electrical systems.

What is Voltage Drop Formula?

A voltage drop formula can help you manually calculate the voltage drop in cables under full load in branch circuits. It does not matter if you are working with copper or aluminum conductors. To accurately calculate the voltage drop for a given cable size, length, and current, you need to know the resistance of the type of cable you’re using. 

✅ V = I × R for DC circuits

✅ Accounts for impedance in AC circuits

✅ Helps ensure safe, efficient electrical design

Use our voltage drop calculator to quickly determine wire size, conductor efficiency, and line loss for safer, more reliable electrical installations.

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To determine voltage drop in an electrical system, engineers and electricians use a standard formula that accounts for conductor resistance, current, and circuit length. The National Electrical Code (NEC) provides guidelines for the maximum voltage drop allowed in various installations to ensure efficiency and safety. For both single-phase and three-phase circuits, excessive voltage drop can lead to poor equipment performance and energy loss. To simplify calculations, a voltage drop calculator can quickly assess whether a circuit meets NEC recommendations and optimize conductor sizing accordingly. You can learn more about how electrical resistance affects circuits in our detailed voltage drop guide, which explains causes, calculations, and solutions for safe, efficient power distribution.

DC / single phase calculation

The voltage drop V in volts (V) is equal to the wire current I in amps (A) times 2 times one way wire size length L in feet (ft) times the wire resistance per 1000 feet R in ohms (Ω/kft) divided by 1000:

Vdrop (V) = Iwire (A) × Rwire(Ω)

= Iwire (A) × (2 × L(ft) × Rwire(Ω/kft) / 1000(ft/kft))

The voltage drop V in volts (V) is equal to the wire current I in amps (A) times 2 times one way wire length L in meters (m) times the wire resistance per 1000 meters R in ohms (Ω/km) divided by 1000:

Vdrop (V) = Iwire (A) × Rwire(Ω)

= Iwire (A) × (2 × L(m) × Rwire (Ω/km) / 1000(m/km))

3 phase calculation

The line-to-line voltage drop V in volts (V) is equal to the square root of 3 times the wire current I in amps (A) times one-way wire length L in feet (ft) times the wire resistance per 1000 feet R in ohms (Ω/kft) divided by 1000:

Vdrop (V) = √3 × Iwire (A) × Rwire (Ω)

= 1.732 × Iwire (A) × (L(ft) × Rwire (Ω/kft) / 1000(ft/kft))

The line-to-line voltage drop V in volts (V) is equal to the square root of 3 times the wire current I in amps (A) times one-way wire length L in meters (m) times the wire resistance per 1000 meters R in ohms (Ω/km) divided by 1000:

Vdrop (V) = √3 × Iwire (A) × Rwire (Ω)

= 1.732 × Iwire (A) × (L(m) × Rwire (Ω/km) / 1000(m/km))

Wire diameter calculations

The n gauge wire diameter, dn in inches (in), is equal to 0.005in times 92 raised to the power of 36 minus gauge number n, divided by 39:

dn (in) = 0.005 in × 92(36-n)/39

The n gauge wire diameter dn in millimetres (mm) is equal to 0.127mm times 92 raised to the power of 36 minus gauge number n, divided by 39:

dn (mm) = 0.127 mm × 92(36-n)/39

Wire cross-sectional area calculations

The n gauge wire's cross-sectional area An in kilo-circular mils (kcmil) is equal to 1000 times the square wire diameter d in inches (in):

An (kcmil) = 1000×dn2 = 0.025 in2 × 92(36-n)/19.5

The n gauge wire's cross-sectional area An in square inches (in2), is equal to pi divided by 4 times the square wire diameter d in inches (in):

An (in2) = (π/4)×dn2 = 0.000019635 in2 × 92(36-n)/19.5

The n gauge wire's cross-sectional area, An, in square millimetres (mm2), is equal to pi divided by 4 times the square wire diameter d in millimetres (mm):

An (mm2) = (π/4)×dn2 = 0.012668 mm2 × 92(36-n)/19.5

Wire resistance calculations

The n gauge wire resistance R in ohms per kilofeet (Ω/kft) is equal to 0.3048×1000000000 times the wire's resistivity ρ in ohm-meters (Ω·m) divided by 25.42 times the cross-sectional area An in square inches (in2):

Rn (Ω/kft) = 0.3048 × 109 × ρ(Ω·m) / (25.42 × An (in2))

The n gauge wire resistance R in ohms per kilometre (Ω/km) is equal to 1000000000 times the wire's resistivity ρ in ohm-meters (Ω·m) divided by the cross-sectional area An in square millimetres (mm2):

Rn (Ω/km) = 109 × ρ(Ω·m) / An (mm2)

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Faraday’s Law describes electromagnetic induction, where changing magnetic fields generate electricity. Discovered in 1831 by Michael Faraday, it revealed how magnetism produces electric current and became the foundation of modern electrical science.

What is Faraday’s Law?

Faraday's Law is a fundamental principle of electromagnetism describing how a changing magnetic field induces an electromotive force (emf) in a conductor. The law: 

✅ Explains electromagnetic induction and induced current

✅ Is essential for transformers, generators, and electric motors

✅ Is the foundation of modern physics and electrical engineering

For a deeper look at the mathematics, mechanisms, and engineering uses, see our detailed guide on Faraday’s Law of Induction."

Michael Faraday, the Inventor of Faraday’s Law

In 1831, Michael Faraday performed experiments with coils of wire, magnets, and galvanometers. He observed that when a magnet was moved through a coil, or when the magnetic field around the coil was changed, a current was generated.

Faraday’s Law proved that electricity could be produced directly from magnetism — a revolutionary concept at the time. Faraday’s experiments were deceptively simple but profoundly important, showing that energy could be converted from one form (mechanical motion of the magnet) into another (electric current). 

Theoretical Context

Faraday’s Law provided one of the first clear demonstrations that electricity and magnetism are not separate forces but part of the same phenomenon. This insight was later formalized by James Clerk Maxwell, whose Maxwell’s equations mathematically unified electromagnetism.

Alongside Ampère’s Law and the Biot–Savart Law, Faraday’s Law gave scientists a new framework to describe the invisible forces of nature. It also introduced the idea of fields, regions of influence surrounding magnets and electrical charges, which became central to modern physics. Read our article titled: Who Invented Electricity for more information about the foundation of electricity.

Understanding Electromagnetic Induction

Faraday’s Law showed that induction can occur in several ways:

• By moving a conductor through a magnetic field

• By changing the strength of a magnetic field

• By altering the orientation or size of the conductor’s loop in the field

In each case, the result is the same: a changing magnetic flux produces an EMF. The direction of the induced current is explained by Lenz’s Law, which states that the induced current always opposes the change that created it, ensuring energy conservation.

The principle of electromagnetic induction is the basis for the operation of various electrical devices, including:

• Generators: These devices convert mechanical energy into electrical energy by rotating a coil within a magnetic field, causing the magnetic flux to change and inducing an EMF in the coil.

• Transformers: Transformers work on the principle of mutual induction, where a changing current in the primary coil produces a varying magnetic field, which in turn induces an EMF in the secondary coil.

• Induction motors: In these motors, a changing magnetic field is created by the stator, inducing an EMF in the rotor conductors, which generates a current that interacts with the magnetic field to produce torque and drive the motor.

Coils, Flux, and Electrodynamics

Faraday’s induction experiments showed that the induced voltage in a coil is equal to the rate of change of magnetic flux through it. This relationship depends on several factors, including the magnetic field strength, the loop area, and the number of turns in the coil. In fact, the induced EMF is proportional to the rate at which a coil of wire cuts across magnetic field lines, meaning that more turns in the coil increase the overall flux linkage.

From the perspective of electrodynamics, this effect illustrates how charges respond to forces within a conductor. The Lorentz force explains why electrons move when exposed to a changing field, while a time-varying field generates a non-conservative electric field that sustains induction. These principles are embedded in the Maxwell–Faraday equation, which extends Faraday’s insight into the framework of Maxwell’s equations.

Faraday also noted that induction is not limited to mutual coupling between separate coils. The principle of self-induction arises when a coil’s own changing current produces an induced EMF opposing the original change. This phenomenon became central to the design of inductors and transformers.

Ultimately, the legacy of Faraday’s Law extends to our understanding of electromagnetic waves. By linking induction with Maxwell’s field theory, Faraday’s Law explains how time-varying fields generate waves that propagate through space — a concept that underpins modern communications and physics.

Why Faraday’s Law Mattered

At the time of its discovery, electricity was known mainly from batteries and static experiments. Faraday’s Law proved that electricity could be generated in continuous and controlled ways. This breakthrough opened the door to inventions that would transform society, from power generation to communication technologies.

Everyday Applications of Faraday’s Law

The importance of Faraday’s Law extends far beyond the laboratory. It forms the basis of countless technologies, including:

• Electric generators – converting mechanical energy into electrical power.

• Transformers – enabling efficient power transmission over long distances.

• Induction motors – powering everything from industrial machines to household appliances.

• Wireless charging systems – transferring energy without physical connections.

• Magnetic storage and security – used in swipe cards and sensors.

• Induction heating and cooktops – converting magnetic energy into heat for practical use.

• Eddy current braking – providing non-contact braking in trains, amusement rides, and industrial systems by inducing currents that resist motion.

• Inductors in circuits – storing energy in magnetic fields and controlling current in electrical systems.

• Wireless energy transfer in EVs – enabling electric vehicles to charge without plugs using electromagnetic induction.

These applications show how Faraday’s 19th-century experiments continue to power the 21st-century world.

Faraday’s Legacy

Faraday’s Law was not just a scientific milestone but also a turning point for technology and industry. Without his insights, there would be no electric power grids, no telecommunications as we know them, and no modern electronics.

The law also highlighted an important principle: that simple experiments can lead to world-changing insights. With little formal education, Faraday reshaped science and technology, showing that careful observation and curiosity could unlock nature’s secrets.

Faraday’s Law remains one of the most important discoveries in physics. By revealing that changing magnetic fields could create electricity, it provided the foundation for modern electrical engineering, industrial power systems, and everyday devices.

Faraday’s Law stands as a reminder that the forces of nature — magnetism, electricity, and motion — are deeply interconnected. Faraday’s insight into electromagnetic induction continues to shape the modern world, demonstrating that a discovery made nearly two centuries ago remains a vital force in our lives today.

Frequently Asked Questions

What did Faraday’s Law prove?

Faraday’s experiments with coils and magnets in 1831 proved that a changing magnetic field can induce an electromotive force (EMF) in a conductor. This showed that electricity can be generated from magnetism, a discovery that revolutionized science and technology.

Why is Faraday’s Law important today?

Faraday’s Law is the foundation of electrical power generation and transmission. It explains how generators, transformers, and induction motors work, making it essential to modern energy systems, communication technologies, and countless everyday devices.

How does Faraday’s Law relate to Maxwell’s equations?

Faraday’s Law was later formalized in Maxwell’s equations as the Maxwell–Faraday equation, which shows that a changing magnetic field produces an electric field. This unification confirmed that electricity and magnetism are two aspects of the same force.

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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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Impedance Definition Explained

Understanding the concept of impedance (Z) is crucial for anyone working with or studying electrical circuits, particularly those involving alternating current (AC). To grasp the intricacies of impedance, it is essential to explore its definition and the various factors that come into play.

The term "impedance" is defined as the opposition that an electrical circuit presents to the flow of an alternating current (AC) or voltage. It is a complex quantity that includes both resistance and reactance components, making it vital in AC circuit analysis. Electrical impedance is essential in determining how electrical energy flows through a circuit, and it is influenced by various factors such as resistance, reactance, and frequency.

Resistance and reactance are two key elements that make up impedance. While resistance is the opposition to the flow of direct current (DC), reactance opposes the flow of AC. Reactance itself is composed of two parts: capacitive and inductive impedance. Capacitive impedance is due to the presence of capacitors in the circuit, while inductive impedance results from the presence of inductors.

Impedance is crucial in AC circuit analysis because it enables engineers and technicians to calculate how AC voltage and current behave within a circuit. This knowledge is necessary when designing and troubleshooting electrical systems. Furthermore, understanding impedance helps identify the optimal conditions for efficient energy transfer, as demonstrated by impedance matching.

Impedance matching refers to adjusting the Z of a source and load to match, maximizing the power transfer between the two. This is essential in various applications such as radio frequency (RF) communications, audio systems, and power transmission.

Calculating the total impedance (Z_total) in a circuit involves considering both the resistive and reactive components. For a series circuit, the total impedance is calculated using Ohm's law as follows:

Z_total = √ (R_total^2 + (X_L - X_C)^2)

Here, Z_total represents total impedance, R_total is the total resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. In parallel circuits, the total impedance is computed by determining the reciprocal of the sum of the reciprocals of individual impedances.

Capacitive and inductive impedance play significant roles in AC circuits. As the frequency of the AC signal changes, the impedance of capacitors and inductors in the circuit also changes. As a result, capacitive impedance decreases with increasing frequency while inductive impedance increases. This characteristic can be utilized to design filters that selectively allow specific frequency ranges to pass through, shaping the output signal as desired.

Impedance spectroscopy is a technique that examines the Z of a material or device over a range of frequencies. This process provides valuable information on the electrical properties and behaviour of the material, enabling researchers and engineers to gain insight into various phenomena such as conductivity, dielectric properties, and electrochemical reactions. This knowledge can be applied to optimize the design and performance of various materials and devices.

Impedance definition and its various aspects, including electrical impedance, complex impedance, impedance matching, and impedance spectroscopy, are essential to understanding AC circuit analysis and the behaviour of electrical circuits in different applications. By examining the interplay of resistance and reactance and the influence of electric and magnetic fields, engineers can design and optimize circuits to ensure maximum efficiency and functionality.

Dynamic electricity is the continuous flow of electric charge—electric current—through a conductor, typically driven by a voltage source. Think of it like water flowing in a pipe, where electrons move uniformly to carry energy.

Active power is the actual energy consumed by electrical equipment to perform useful work, such as lighting or running motors. It is measured in kilowatts (kW) and is essential for efficient power system design, load management, and energy billing accuracy.

What is "active power"?

Active power is the real power consumed in an AC circuit to perform useful work.

✅ Measured in kilowatts (kW)

✅ Powers resistive loads like heaters, lights, and motors

✅ Crucial for calculating energy usage and efficiency

In AC circuits, active power (P) refers to the component of electrical power that results in energy transfer to a load. It is the energy that performs work—such as producing motion, light, or heat—and is distinct from reactive power, which oscillates between source and load without being consumed.

Active Power Formula

The general formula for active power is:

P = VIcosθ

Where:

• P = Active Power (watts)

• V = RMS Voltage

• I = RMS Current

• θ = Phase angle between voltage and current

In real-world power systems, only the portion of the current in phase with the voltage contributes to active power. The portion out of phase results in reactive power and does not produce usable energy.

Equation 1

The above active power equation is valid for both sinusoidal and nonsinusoidal conditions. For sinusoidal condition, '1rn, resolves to the familiar form,

Equation 2

Sinusoidal and Non-Sinusoidal Conditions

The calculation of active power can differ slightly depending on waveform distortion:

• For sinusoidal conditions, Equation 1 simplifies to the standard P = VIcosθ form.

• For non-sinusoidal waveforms, the total active power includes the sum of contributions from all harmonic components. However, since voltage distortion is typically below 5% in most power systems, the simplified equation is usually accurate enough for practical purposes.

Real-World Example

A standard incandescent light bulb converts electrical power into visible light and heat. This is a classic case of active power at work—where the current and voltage are in phase, and virtually all supplied power is consumed usefully.

Active vs Reactive vs Apparent Power

It’s important to distinguish active power from related concepts:

• Reactive Power (Q): Energy exchanged but not consumed, measured in kVAR.

• Apparent Power (S): The vector sum of active and reactive power, measured in kVA.

• Power Factor: The ratio of active power to apparent power (PF = P/S).

While active power does the real work, apparent power impacts system loading and reactive power affects voltage stability. See our power factor training for more.

Measurement and Application

Active power is typically measured using true RMS meters that calculate the average of the instantaneous product of voltage and current. Advanced power analyzers now offer direct measurement of real power in both clean and distorted systems.

Engineers use active power data for:

• Energy consumption analysis

• Load management and optimization

• System efficiency evaluation

• Compliance with energy standards

Related Reading

• Understand the difference between active and reactive power

• Learn how to improve system performance with our power quality analysis training

• Discover how electrical resistance affects power consumption

• Explore the role of power factor correction in reducing energy waste

Frequently Asked Questions

What is active power used for?

Active power is used to perform real work in electrical systems, such as lighting, heating, and running motors.

Is active power the same as real power?

Yes. Active power, real power, and true power are interchangeable terms that refer to the same concept.

How is active power calculated?

It is calculated using the formula P = VIcosθ, where V and I are RMS voltage and current, and θ is the phase angle between them.

In summary, understanding active power is essential for designing efficient electrical systems and ensuring energy accountability. By distinguishing it from reactive and apparent power, professionals can improve system performance and reduce energy losses.

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