Electronic Circuit Formulas

Contents

Notation

C E G I i L M

capacitance voltage source conductance current instantaneous current inductance mutual inductance

(Farads) (Volts) (Siemens) (Amps) (Amps) (Henrys) (Henrys)

P Q R t V v W

power charge resistance time voltage drop instantaneous voltage energy

(Watts) (Coulombs) (Ohms) (seconds) (Volts) (Volts) (Joules)

Resistance

Resistances in Series

Voltage Division by Series Resistances

The voltages V₁ and V₂ which appear across the respective resistances R₁ and R₂ are:
V₁ = I_SR₁ = E_SR₁ / (R₁ + R₂)
V₂ = I_SR₂ = E_SR₂ / (R₁ + R₂)

Resistances in Parallel

Alternatively, when conductances G₁, G₂, G₃, ... are connected in parallel, the total conductance G_P is:
G_P = G₁ + G₂ + G₃ + ...
where G = 1 / R

For two resistances R₁ and R₂ connected in parallel, the total resistance R_P is:
R_P = R₁R₂ / (R₁ + R₂)
R_P = product / sum

The resistance R₂ to be connected in parallel with resistance R₁ to give a total resistance R_P is:
R₂ = R₁R_P / (R₁ - R_P)
R₂ = product / difference

Current Division by Parallel Resistances

The currents I₁ and I₂ which pass through the respective resistances R₁ and R₂ are:
I₁ = V_P / R₁ = I_PR₂ / (R₁ + R₂)
I₂ = V_P / R₂ = I_PR₁ / (R₁ + R₂)

Capacitance

Alternatively, by differentiation with respect to time:
dQ/dt = I = C dV/dt

The capacitance C of a circuit is equal to the charge divided by the voltage:
C = Q / V = òidt / V

Alternatively, the capacitance C of a circuit is equal to the current divided by the rate of change of voltage:
C = I / (dV/dt) = (dQ/dt) / (dV/dt) = dQ/dV

Capacitances in Series

Capacitances in Parallel

Inductance

The inductance L of a circuit is equal to the induced voltage divided by the rate of change of current:
L = - E / (di/dt)

The mutual inductance M of two coupled inductances L₁ and L₂ is equal to the mutually induced voltage in one inductance divided by the rate of change of current in the other inductance:
M = - E₁ / (di₂/dt)
M = - E₂ / (di₁/dt)
If the coupling between the two inductances is perfect, then:
M = (L₁L₂)^½

Inductances in Series

When two coupled inductances L₁ and L₂ with mutual inductance M are connected in series, the total inductance L_S is:
L_S = L₁ + L₂ ± 2M
The plus or minus sign indicates that the coupling is either additive or subtractive, depending on the connection polarity.

Inductances in Parallel

Time Constants

If a voltage E is applied to a series circuit comprising a discharged capacitance C and a resistance R, then after time t the current i, the voltage v_R across the resistance and the voltage v_C across the capacitance are:
i = (E / R)e ^{- t / CR}
v_R = iR = Ee ^{- t / CR}
v_C = E - v_R = E(1 - e ^{- t / CR})

Inductance and resistance
The time constant of an inductance L and a resistance R is equal to L / R, and represents the time to change the current in the inductance from zero to E / R at a constant rate of change of current E / L (which produces an induced voltage E across the inductance).

If a voltage E is applied to a series circuit comprising a pure inductance L and a resistance R, then after time t the current i, the voltage v_R across the resistance and the voltage v_L across the inductance are:
i = (E / R)(1 - e ^{- tR / L})
v_R = iR = E(1 - e ^{- tR / L})
v_L = E - v_R = Ee ^{- tR / L}

Power

Energy

The energy W consumed by a resistance R carrying a current I due to a voltage E is:
W = E²t / R = EIt = I²Rt

The energy W stored in a capacitance C holding a voltage V is:
W = ½CV²

The energy W stored in an inductance L carrying a current I is:
W = ½LI²

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