Electrical Engineering Formulas Online

## Ohm’s Law (Relation between Voltage, Current, Resistance)

**V = I * R**

Ohm’s Law relates relationship between voltage (V), current (I), and

resistance (R) in an electrical circuit.

## Power (Relation between Voltage, Current)

**P = V * I**

Power (P) is the product of voltage (V) and current (I) and represents the

rate at which energy is transferred.

## Energy (Relation between Power, Time)

**E = P * t**

Energy (E) is the product of power (P) and time (t) and represents the total

amount of energy consumed or produced.

## Series Resistors Formula

**R _{total} = R_{1} + R_{2} + R_{3} + … R_{n}**

The total resistance (R_{total}) in a series circuit is the sum of

individual resistances (R_{1}, R_{2}, R_{3}, …, R_{n}).

## Parallel Resistors Formula

**1/R _{total} = 1/R_{1} + 1/R_{2} + 1/R_{3}**

+ … 1/R_{n}

The total resistance (R

_{total}) in a parallel circuit is the

reciprocal of the sum of the reciprocals of individual resistances (R

_{1},

R

_{2}, R

_{3}, …R

_{n}).

## Voltage Divider Rule

**V _{out} = (R_{2} / (R_{1} + R_{2})) * V_{in}**

The voltage divider formula calculates the output voltage (V

_{out})

based on the input voltage (V

_{in}) and the resistances (R

_{1},

R

_{2}) in a series circuit.

## Current Divider Rule

**I _{out} = (R_{2} / (R_{1} + R_{2})) * I_{in}**

The current divider formula calculates the output current (I

_{out})

based on the input current (I

_{in}) and the resistances (R

_{1},

R

_{2}) in a parallel circuit.

## Kirchhoff’s Current Law (KCL Formula)

**ΣI _{in} = ΣI_{out}**

Kirchhoff’s Current Law states that the sum of currents entering a node is

equal to the sum of currents leaving the node in a circuit.

## Kirchhoff’s Voltage Law (KVL Formula)

**ΣV _{loop} = 0**

Kirchhoff’s Voltage Law states that the sum of voltage drops around any closed

loop in a circuit is equal to zero.

## Capacitance (Relationship between Charge and Voltage)

**Q = C * V**

Capacitance (C) is the ratio of the charge (Q) stored on a capacitor to the

voltage (V) across it.

## Energy Stored in a Capacitor

**E = (1/2) * C * V ^{2}**

The energy (E) stored in a capacitor is proportional to the square of the

voltage (V) across it and the capacitance (C).

## Inductance (Flux Linkage, Current)

**Ψ = L * I**

Inductance (L) is the ratio of the magnetic flux linkage (Ψ) through an

inductor to the current (I) flowing through it.

## Energy Stored in an Inductor

**E = (1/2) * L * I ^{2}**

The energy (E) stored in an inductor is proportional to the square of the

current (I) flowing through it and the inductance (L).

## RC Time Constant Formula

**τ = R * C**

The RC time constant (τ) is the time it takes for a capacitor to charge or

discharge to approximately 63.2% of its final voltage in an RC circuit.

## RL Time Constant Formula

**τ = L / R**The RL time constant (τ) is the time it takes for the current in an

inductor to reach approximately 63.2% of its final value when an RL circuit is

energized.

## Active Power (Real Power Formula)

**P = V * I * cos(θ)**

Active power (P) represents the actual power consumed or produced in an

electrical circuit and is the product of voltage (V), current (I), and the

power factor (cos(θ)).

## Reactive Power Formula

**Q = V * I * sin(θ)**Reactive power (Q) represents the power oscillations between the source and

reactive components of a circuit and is the product of voltage (V), current

(I), and the sine of the phase angle (sin(θ)).

## Apparent Power Formula

**S = V * I**

Apparent power (S) is the product of voltage (V) and current (I) in an AC

circuit and represents the total power supplied or consumed, combining active

and reactive power.

## Power Factor Formula

**PF = cos(θ)**

Power factor (PF) is the cosine of the phase angle (θ) between the voltage

and current waveforms in an AC circuit and indicates the efficiency of power

usage.

## Peak to RMS Voltage (Root Mean Square)

**V _{rms} = V_{peak}/√2**

RMS voltage (Vrms) is the effective or equivalent voltage of an AC waveform and

is calculated by dividing the peak voltage (Vpeak) by the square root of 2.

## Peak to RMS Current (Root Mean Square)

**Irms = Ipeak / √2**

RMS current (Irms) is the effective or equivalent current of an AC waveform and

is calculated by dividing the peak current (Ipeak) by the square root of 2.

## Impedance (Resistance, Reactance)

**Z = √(R ^{2} + X^{2})**

Impedance (Z) represents the total opposition to current flow in an AC circuit

and is the vector sum of resistance (R) and reactance (X).

## Capacitive Reactance

**X _{c} = 1 / (2πfC)**

Capacitive reactance (Xc) is the opposition to AC current flow offered by a

capacitor and is inversely proportional to frequency (f) and capacitance (C).

## Inductive Reactance

**X _{l} = 2πfL**

Inductive reactance (Xl) is the opposition to AC current flow offered by an

inductor and is directly proportional to frequency (f) and inductance (L).

## Resonant Frequency

**f _{r} = 1 / (2π√(LC))**

Resonant frequency (fr) is the frequency at which the capacitive reactance (Xc)

and inductive reactance (Xl) in a series LC circuit cancel each other out.

## Decibel (dB)

**dB = 10 * log10(P/Pref)**

The decibel (dB) is a logarithmic unit used to express power (P) or voltage

ratios

## dBm (Decibel-milliwatt)

**P(dBm) = 10 * log10(P(mW)/1mW)**

dBm is a unit of power measurement relative to 1 milliwatt (mW) and is often

used to express power levels in communication systems.

## Wheatstone Bridge (Unknown Resistance)

**Rx = R2 * (R1/R3)**

The Wheatstone Bridge formula calculates the unknown resistance (Rx) in a

balanced bridge circuit based on the known resistances R1, R2, and R3.

## Maximum Power Transfer Theorem

R_{load} = R_{source}

According to the Maximum Power Transfer Theorem, maximum power is transferred

from a source to a load when the resistance of the load (R_load) matches the

internal resistance of the source (R_source).

## Mutual Inductance (Induced Voltage, Current)

V_{2} = M * dI1/dt

Mutual inductance (M) represents the coupling between two inductors, and it is

the ratio of the induced voltage (V2) in the second inductor to the rate of

change of current (dI1/dt) in the first inductor.

## Three-Phase Power (Apparent Power, Voltage, Current, Power Factor)

S = √3 * V * I * PF

Three-phase power (S) is the product of the square root of 3 (√3), line-to-line

voltage (V), line current (I), and power factor (PF).

## Power Transformer Turns Ratio

**(Vp/Vs) = (Np/Ns)**

The turns ratio of a power transformer is given by the ratio of primary

voltage (Vp) to secondary voltage (Vs), which is equal to the ratio of the

number of turns in the primary winding (Np) to the number of turns in the

secondary winding (Ns).

## Voltage Regulation

**Voltage Regulation = (Vnl – Vfl) / Vfl * 100%**

Voltage regulation measures the percentage change in output voltage from

no-load (Vnl) to full-load (Vfl) conditions in a power system, indicating the

ability of the system to maintain a stable voltage level.

## Faraday’s Law of Electromagnetic Induction

**E = -dΦ/dt**

Faraday’s Law states that the electromotive force (EMF) induced in a circuit

is equal to the negative rate of change of magnetic flux (Φ) with respect to

time (t).

## Shannon-Hartley Theorem (Channel Capacity)

**C = B * log _{2}(1 + S/N)**

The Shannon-Hartley theorem relates the channel capacity (C) in bits per second

(bps) to the bandwidth (B) and the signal-to-noise ratio (S/N) in a

communication system.

## Gain

**Gain = Output / Input**Gain represents the amplification factor of a system and is the ratio of

the output voltage or current to the input voltage or current.

## Voltage Regulator Efficiency

**Efficiency = (Output Power / Input Power) * 100%**

The efficiency of a voltage regulator is the ratio of the output power to the

input power, expressed as a percentage, indicating how effectively the

regulator converts input power to usable output power.

## Power Factor & Power Factor Correction

**Power Factor = (Real Power / Apparent Power)**

Power factor correction is the process of adjusting the electrical system to

achieve a power factor closer to unity (1) and minimize reactive power,

improving the overall efficiency of power usage.

## Step-Up Transformer

Vs / Vp = Ns / Np

A step-up transformer increases the voltage level from the primary (input)

side (Vp) to the secondary (output) side (Vs) based on the turns ratio (Ns /

Np).

## Step-Down Transformer

Vs / Vp = Ns / Np

A step-down transformer decreases the voltage level from the primary (input)

side (Vp) to the secondary (output) side (Vs) based on the turns ratio (Ns /

Np).

## Maximum Efficiency of a Transformer

Efficiency_max = (Vs * Is) / (Vs * Is + Pcu)

The maximum efficiency of a transformer occurs when the copper losses (Pcu) are

equal to the product of the secondary voltage (Vs) and secondary current (Is).

Power Triangle

The power triangle is a graphical representation that shows the

relationships between real power (P), reactive power (Q), apparent power (S),

and power factor (PF) in an AC circuit.

## Two-Port Network Parameters

Two-port network parameters (also known as ABCD parameters) are a set of

four parameters used to characterize the behavior of a two-port network in

terms of voltage and current relationships.

## Voltage Drop (Ohmic)

**V = I * R**

Ohmic voltage drop (V) across a resistor is the product of the current (I)

flowing through it and the resistance (R).

## Voltage Drop (Transmission Line)

**V = I * Z**

The voltage drop (V) along a transmission line is the product of the current

(I) flowing through it and the impedance (Z) of the line.

## Resistor Power Dissipation

**P = I ^{2} * R**

The power dissipated by a resistor (P) is given by the product of the square

of the current (I) passing through it and the resistance (R) of the resistor.

## Inductor Energy Storage

**Energy = (1/2) * L * I ^{2}**

The energy stored in an inductor is given by half the product of the

inductance (L) and the square of the current (I) flowing through it.

## Capacitor Energy Storage

Energy = (1/2) * C * V^{2}

The energy stored in a capacitor is given by half the product of the

capacitance (C) and the square of the voltage (V) across it.

## Op-Amp Voltage Gain

**Voltage Gain = -(Rf / Rin)**

The voltage gain of an operational amplifier (op-amp) in an inverting

configuration is given by the ratio of the feedback resistor (Rf) to the input

resistor (Rin), with a negative sign indicating inversion.

## Op-Amp Non-Inverting Voltage Gain

**Voltage Gain = 1 + (Rf / Rin)**

The voltage gain of an operational amplifier (op-amp) in a non-inverting

configuration is given by the ratio of the feedback resistor (Rf) to the input

resistor (Rin), plus 1.

## Op-Amp Inverting Amplifier

**Vout = -(Vin) * (Rf / Rin)**

The output voltage (Vout) of an inverting amplifier using an operational

amplifier (op-amp) is given by the negative input voltage (Vin) multiplied by

the ratio of the feedback resistor (Rf) to the input resistor (Rin).

## Op-Amp Non-Inverting Amplifier

**Vout = Vin * (1 + (Rf / Rin))**

The output voltage (Vout) of a non-inverting amplifier using an operational

amplifier (op-amp) is given by the input voltage (Vin) multiplied by the sum of

1 and the ratio of the feedback resistor (Rf) to the input resistor (Rin).

## Op-Amp Summing Amplifier

**Vout = -(V1 * R1 / Rin1) – (V2 * R2 / Rin2) – …**

The output voltage (Vout) of a summing amplifier using an operational

amplifier (op-amp) is the sum of the weighted input voltages (V1, V2, …)

multiplied by their respective ratios with the input resistors (R1, R2, …)

divided by the input resistors (Rin1, Rin2, …).

## Op-Amp Integrator

**Vout = -(1 / (Rf * C)) * ∫(Vin dt)**

The output voltage (Vout) of an integrator circuit using an operational

amplifier (op-amp) is proportional to the negative integral of the input

voltage (Vin) with respect to time, with the proportionality constant

determined by the feedback resistor (Rf) and the capacitor (C).

## Op-Amp Differentiator

**Vout = -(Rf * C) * d(Vin) / dt**

The output voltage (Vout) of a differentiator circuit using an operational

amplifier (op-amp) is proportional to the negative derivative of the input

voltage (Vin) with respect to time, with the proportionality constant

determined by the feedback resistor (Rf) and the capacitor (C).

## RMS Voltage (Root Mean Square)

**Vrms = √(V1^2 + V2^2 + … + Vn^2) / n**

The RMS voltage is the square root of the average of the squares of a set of

voltages (V1, V2, …, Vn), where n is the total number of voltages.

## RMS Current (Root Mean Square)

Irms = √(I1^2 + I2^2 + … + In^2) / n

The RMS current is the square root of the average of the squares of a set of

currents (I1, I2, …, In), where n is the total number of currents.

## Complex Power

S = P + jQ

Complex power (S) is a phasor quantity that represents the combination of real

power (P) and reactive power (Q) in an AC circuit.

## Power Factor Correction (Capacitive)

C = (Q / (ω * V^2))

The capacitance (C) required for power factor correction in an AC circuit is

given by the reactive power (Q) divided by the product of the angular frequency

(ω) and the square of the voltage (V).

## Power Factor Correction (Inductive)

L = (Q / (ω * V^2))

The inductance (L) required for power factor correction in an AC circuit is

given by the reactive power (Q) divided by the product of the angular frequency

(ω) and the square of the voltage (V).

## Inductor Quality Factor (Q Factor)

Q = (ω * L) / R

The quality factor (Q) of an inductor is the ratio of its inductive reactance

(ωL) to its resistance (R), indicating the efficiency of energy storage in the

inductor.

## Capacitor Quality Factor (Q Factor)

Q = (1) / (ω * R * C)

The quality factor (Q) of a capacitor is the reciprocal of the product of the

angular frequency (ω), the resistance (R),

## Capacitor Quality Factor (Q Factor) (continued)

Q = (1) / (ω * R * C)

The quality factor (Q) of a capacitor is the reciprocal of the product of the

angular frequency (ω), the resistance (R), and the capacitance (C). It

represents the efficiency of energy storage and release in the capacitor.

## Resonant Frequency (Series RLC Circuit)

ω = 1 / √(L * C)

The resonant frequency (ω) of a series RLC circuit is inversely proportional to

the square root of the product of the inductance (L) and capacitance (C). It

represents the frequency at which the circuit exhibits maximum impedance.

## Bandwidth (Series RLC Circuit)

BW = ωr / Q

The bandwidth (BW) of a series RLC circuit is determined by the resonant

frequency (ωr) divided by the quality factor (Q). It represents the range of

frequencies over which the circuit response is significant.

## Resistor Color Code

The resistor color code is a system of marking resistors with colored bands

that represent their resistance values, tolerance, and sometimes temperature

coefficient.

## Kirchhoff’s Laws

Kirchhoff’s laws are fundamental principles used to analyze electrical

circuits:

## Kirchhoff’s Current Law (KCL)

The algebraic sum of currents entering a node is zero.

## Kirchhoff’s Voltage Law (KVL)

The algebraic sum of voltages around any closed loop in a circuit is zero.

Maximum Power Transfer Theorem for DC**R _{load} = R_{source}**

According to the Maximum Power Transfer Theorem for DC circuits, the load

resistance (R_{load}) should be equal to the source resistance (R_{source})

to achieve maximum power transfer.

## Thevenin’s Theorem

Thevenin’s theorem states that any linear electrical network with voltage

and current sources and resistors can be replaced by an equivalent circuit

consisting of a single voltage source (Thevenin voltage) in series with a

single resistor (Thevenin resistance).