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
Rtotal = R1 + R2 + R3 + … Rn
The total resistance (Rtotal) in a series circuit is the sum of
individual resistances (R1, R2, R3, …, Rn).
Parallel Resistors Formula
1/Rtotal = 1/R1 + 1/R2 + 1/R3
+ … 1/Rn
The total resistance (Rtotal) in a parallel circuit is the
reciprocal of the sum of the reciprocals of individual resistances (R1,
R2, R3, …Rn).
Voltage Divider Rule
Vout = (R2 / (R1 + R2)) * Vin
The voltage divider formula calculates the output voltage (Vout)
based on the input voltage (Vin) and the resistances (R1,
R2) in a series circuit.
Current Divider Rule
Iout = (R2 / (R1 + R2)) * Iin
The current divider formula calculates the output current (Iout)
based on the input current (Iin) and the resistances (R1,
R2) in a parallel circuit.
Kirchhoff’s Current Law (KCL Formula)
ΣIin = ΣIout
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)
ΣVloop = 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 * V2
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 * I2
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)
Vrms = Vpeak/√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 = √(R2 + X2)
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
Xc = 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
Xl = 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
fr = 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
Rload = Rsource
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)
V2 = 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 * log2(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 = I2 * 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 * I2
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 * V2
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
Rload = Rsource
According to the Maximum Power Transfer Theorem for DC circuits, the load
resistance (Rload) should be equal to the source resistance (Rsource)
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).