Electronics & Circuits

Circuit analysis, components, signals and digital logic formulae

Explore the essential formulas for understanding how circuits behave, from Ohm’s Law and electrical power to resistors, capacitors, inductors, and reactance. This category is useful for students, exam preparation, and anyone working with electronics, helping you calculate voltages, currents, resistance, energy, and signal response so you can analyze and design circuits with confidence.

Ohm's Law

V = IR

Voltage equals current times resistance.

Electrical Power (VI)

P = VI

Power dissipated by a component.

Power (I²R)

P = I^2 R

Power lost as heat in a resistor.

Power (V²/R)

P = \frac{V^2}{R}

Power from voltage and resistance.

Resistors in Series

R_{eq} = R_1 + R_2 + \cdots

Series resistances add directly.

Resistors in Parallel

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots

Reciprocals of parallel resistances add.

Capacitors in Parallel

C_{eq} = C_1 + C_2 + \cdots

Parallel capacitances add.

Capacitors in Series

\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots

Reciprocals of series capacitances add.

Capacitance

C = \frac{Q}{V}

Charge stored per unit voltage.

Capacitor Energy

E = \tfrac{1}{2}CV^2

Energy stored in a capacitor.

Inductor Energy

E = \tfrac{1}{2}LI^2

Energy stored in a magnetic field.

Capacitive Reactance

X_C = \frac{1}{2\pi f C}

Opposition of a capacitor to AC.

Inductive Reactance

X_L = 2\pi f L

Opposition of an inductor to AC.

Impedance (RLC)

Z = \sqrt{R^2 + (X_L - X_C)^2}

Total opposition in an AC circuit.

Resonant Frequency

f_0 = \frac{1}{2\pi\sqrt{LC}}

Frequency at which an LC circuit resonates.

RC Time Constant

\tau = RC

Time to charge a capacitor to ~63%.

RL Time Constant

\tau = \frac{L}{R}

Time constant of an inductor-resistor circuit.

Voltage Divider

V_{out} = V_{in}\frac{R_2}{R_1 + R_2}

Output voltage from two series resistors.

Current Divider

I_1 = I\frac{R_2}{R_1 + R_2}

Current split between two parallel resistors.

Kirchhoff's Voltage Law

\sum V = 0

Voltages around any closed loop sum to zero.

Kirchhoff's Current Law

\sum I_{in} = \sum I_{out}

Current into a node equals current out.

RMS Voltage

V_{rms} = \frac{V_{peak}}{\sqrt{2}}

Effective value of a sinusoidal voltage.

AC Real Power

P = VI\cos\phi

Real power with a phase angle between V and I.

Decibel (Power)

dB = 10\log_{10}\frac{P_2}{P_1}

Power ratio expressed in decibels.

Decibel (Voltage)

dB = 20\log_{10}\frac{V_2}{V_1}

Voltage ratio in decibels.

Transformer Turns Ratio

\frac{V_p}{V_s} = \frac{N_p}{N_s}

Voltage ratio equals turns ratio.

Inverting Amplifier Gain

A_v = -\frac{R_f}{R_{in}}

Gain of an inverting op-amp.

Non-Inverting Gain

A_v = 1 + \frac{R_f}{R_{in}}

Gain of a non-inverting op-amp.

LED Series Resistor

R = \frac{V_s - V_f}{I}

Resistor to safely drive an LED.

Charge from Current

Q = It

Charge transferred by a steady current.

Drift Velocity

v_d = \frac{I}{nAq}

Average velocity of charge carriers.

Wire Resistance

R = \frac{\rho L}{A}

Resistance from resistivity, length and area.

Nyquist Bit Rate

C = 2B\log_2 M

Maximum data rate of a noiseless channel.

AND Gate

Y = A \cdot B

Output is 1 only when both inputs are 1.

OR Gate

Y = A + B

Output is 1 if either input is 1.

XOR Gate

Y = A \oplus B

Output is 1 when inputs differ.

Apparent Power

S = \sqrt{P^2 + Q^2}

Combination of real and reactive power.

Resonant Frequency

f_0 = \frac{1}{2\pi\sqrt{LC}}

Frequency where an LC circuit resonates.

Quality Factor

Q = \frac{f_0}{\Delta f}

Sharpness of a resonant peak.

Capacitor Energy

E = \frac{1}{2}CV^2

Energy stored in a capacitor.

Inductor Energy

E = \frac{1}{2}LI^2

Energy stored in an inductor magnetic field.

Capacitor Charge

Q = CV

Charge stored on a capacitor.

Current from Charge

I = \frac{Q}{t}

Current as the rate of charge flow.

LED Series Resistor

R = \frac{V_s - V_f}{I}

Resistor to safely drive an LED.

Wheatstone Bridge Balance

\frac{R_1}{R_2} = \frac{R_3}{R_4}

Condition for a balanced measurement bridge.

Voltage Divider Output

V_{out} = V_{in}\frac{R_2}{R_1 + R_2}

Output of a two-resistor divider.