Circuits & Electrical Power formula sheet — printable

Ohm's Law

V = I R

Electric Charge (Q = It)

Q = I t

Electrical Power (P = VI)

P = V I

Electrical Power (P = I²R)

P = I^{2} R

Electrical Power (P = V²/R)

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

Two Resistors in Series

R_{t} = R_{1} + R_{2}

Two Resistors in Parallel

R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

Voltage Divider

V_{out} = V_{in} \frac{R_{2}}{R_{1} + R_{2}}

Current Divider

I_{1} = I_{t} \frac{R_{2}}{R_{1} + R_{2}}

Resistance of a Wire (R = ρL/A)

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

Conductor Resistance Temperature Correction

R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]

Kirchhoff's Voltage Law (Three-Element Loop)

V_{s} = V_{1} + V_{2} + V_{3}

Kirchhoff's Current Law (Node with Three Branches)

I_{in} = I_{1} + I_{2} + I_{3}

Thevenin Resistance from an Open-Circuit and Loaded Measurement

R_{Th} = R_{L} \left( \frac{V_{OC}}{V_{L}} - 1 \right)

Norton Current from the Thevenin Equivalent

I_{N} = \frac{V_{Th}}{R_{Th}}

Maximum Power Transfer to a Matched Load

P_{max} = \frac{V_{Th}^{2}}{4 R_{Th}}

Delta to Wye Resistance Transformation

R_{A} = \frac{R_{ab} R_{ca}}{R_{ab} + R_{bc} + R_{ca}}

Wye to Delta Resistance Transformation

R_{ab} = \frac{R_{A} R_{B} + R_{B} R_{C} + R_{C} R_{A}}{R_{C}}

LED Series Resistor

R = \frac{V_{s} - V_{f}}{I}

Capacitance (C = Q/V)

C = \frac{Q}{V}

Energy Stored in a Capacitor

E = \tfrac{1}{2} C V^{2}

Two Capacitors in Series

C_{t} = \frac{C_{1} C_{2}}{C_{1} + C_{2}}

Two Capacitors in Parallel

C_{t} = C_{1} + C_{2}

RC Time Constant

\tau = R C

RC Capacitor Discharge

V = V_{0} \, e^{-t/\tau}

RL Time Constant (τ = L/R)

\tau = \frac{L}{R}

Energy Stored in an Inductor

E = \tfrac{1}{2} L I^{2}

RMS and Peak Voltage

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

Inductive Reactance (X_L = 2πfL)

X_L = 2\pi f L

Capacitive Reactance (X_C = 1/2πfC)

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

Series RL or RC Impedance

Z = \sqrt{R^{2} + X^{2}}

Series RLC Impedance

Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}

Phase Angle from Power Factor

\varphi = \arccos(\text{PF})

LC Resonant Frequency

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

Q Factor of a Series Resonant Circuit

Q = \frac{1}{R} \sqrt{\frac{L}{C}}

Bandwidth from Q and Centre Frequency

BW = \frac{f_{0}}{Q}

RC Cutoff Frequency

f_{c} = \frac{1}{2\pi R C}

RL Cutoff Frequency

f_{c} = \frac{R}{2\pi L}

Decibel Voltage Gain

G_{dB} = 20 \log_{10}\!\left(\frac{V_{2}}{V_{1}}\right)

Decibel Power Gain

G_{dB} = 10 \log_{10}\!\left(\frac{P_{2}}{P_{1}}\right)

Single-Phase Real Power with Power Factor

P = V I \, \text{PF}

Power Factor from Real and Apparent Power

\text{PF} = \frac{P}{S}

Reactive Power (Power Triangle)

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

Three-Phase Real Power

P = \sqrt{3} \, V_{L} I_{L} \, \text{PF}

Three-Phase Apparent Power

S = \sqrt{3} \, V_{L} I_{L}

Wye Line and Phase Voltage

V_{L} = \sqrt{3} \, V_{\varphi}

Delta Line and Phase Current

I_{L} = \sqrt{3} \, I_{\varphi}

Power-Factor Correction kvar

Q_{c} = P \left( \tan\varphi_{1} - \tan\varphi_{2} \right)

Power-Factor Correction Capacitance

C = \frac{Q_{c}}{2\pi f V^{2}}

Electrical Energy (E = Pt)

E = P t

Energy Cost from a Utility Rate

C_e = E \, p_e

Voltage Drop, Single Phase

V_{d} = \frac{2 \rho L I}{A}

Voltage Drop, Three Phase

V_{d} = \frac{\sqrt{3} \, \rho L I}{A}

Percent Voltage Drop

\%V_{d} = \frac{100 \, V_{d}}{V_{s}}

Peukert's Law (Battery Runtime)

t = H \left( \frac{C}{I H} \right)^{k}

Synchronous Speed from Frequency and Poles

N_{s} = \frac{2f}{p}

Induction Motor Slip

s = \frac{100 \, (N_{s} - N_{r})}{N_{s}}

Motor Torque from Power and Speed

T = \frac{P}{2\pi N}

Motor Efficiency

\eta = \frac{100 \, P_{out}}{P_{in}}

Three-Phase Motor Full-Load Current

I = \frac{P_{out}}{\sqrt{3} \, V \, \text{PF} \, \eta}

Motor Locked-Rotor Starting Current

I_{LR} = \frac{1000 \, k \, P}{\sqrt{3} \, V}

Transformer Voltage Ratio

\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}

Transformer Full-Load Current

I_{FL} = \frac{S}{k \, V}

Voltage Regulation

\%VR = \frac{100 \, (V_{nl} - V_{fl})}{V_{fl}}

Transformer Percent-Impedance Voltage Drop

V_{d} = \frac{\%Z}{100} \cdot \frac{S_{L}}{S_{R}} \cdot V_{R}

Available Short-Circuit Current from Percent Impedance

I_{SC} = \frac{100 \, I_{FL}}{\%Z}

Generator Sizing from Connected Load

P_{g} = P_{c} \, D_{f} \left( 1 + m \right)

Coulomb's Law

F = \frac{k_e \, q_{1} q_{2}}{r^{2}}

Magnetic Force on a Moving Charge

F = q v B \sin\theta

Magnetic Force on a Current-Carrying Wire

F = B I L \sin\theta

Force Between Parallel Wires

F = \frac{\mu_0 I_1 I_2 \ell}{2\pi d}

Magnetic Field of a Solenoid

B = \frac{\mu_0 N I}{L}

Magnetic Flux (Φ = BA cos θ)

\Phi = B A \cos\theta

Faraday's Law of Induction

\varepsilon = N \frac{\Delta\Phi}{\Delta t}

Motional EMF (ε = BLv)

\varepsilon = B L v