Electronics &amp; Circuits

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.