Cheat sheet

Every formula, one page

41 formulas across 6 chapters, KaTeX-rendered. Search by name, formula or chapter — or hit ⌘/Ctrl + F for browser find.

Chapter 1

Basic Concepts

Study

Current

i = \frac{d q}{d t}

[Amperes (A)]

Voltage

v = \frac{d w}{d q}

[Volts (V)]

Power

p = \frac{d w}{d t} = v \cdot i

[Watts (W)]

Energy

w = \int p d t

[Joules (J)]

Energy (kWh)

W = P \times t

[kWh]

Chapter 2

Basic Laws

Study

Ohm's Law

v = i R

[V]

Resistance

R = ρ L / A

[Ohms (Ω)]

KCL

\sum i_{in} = \sum i_{o u t}

[A]

KVL

\sum v = 0 (a ro u n d an yc l ose d l oo p)

[V]

Series Resistance

R_{e q} = R_{1} + R_{2} + \dots + R_{n}

[Ω]

Parallel Resistance

\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots + \frac{1}{R _{n}}

[Ω]

Voltage Divider

v_{1} = \frac{R _{1}}{R _{1} + R _{2}} v

[V]

Current Divider

i_{1} = \frac{R _{2}}{R _{1} + R _{2}} i

[A]

Y to Δ

R_{a} = \frac{R _{1} R _{2} + R _{2} R _{3} + R _{3} R _{1}}{R _{1}}

[Ω]

Δ to Y

R_{1} = \frac{R _{a} R _{b}}{R _{a} + R _{b} + R _{c}}

[Ω]

Chapter 3

Methods of Analysis

Study

Nodal Analysis (KCL at node)

\sum (v_{n} - v_{k}) / R_{nk} = I_{n}

[A]

Mesh equation (KVL)

\sum (R_{ij} \times i_{j}) = \sum v_{so u rces}

[V]

Conductance matrix

G V = I

[A]

Resistance matrix

R I = V

[V]

Chapter 4

Circuit Theorems

Study

Superposition

v = v_{1} + v_{2} + \dots (o n eso u rce a t a t im e)

[V]

Thévenin Voltage

V_{T h} = V_{oc} (o p e n - c i rc u i t v o lt a g e)

[V]

Thévenin Resistance

R_{T h} = V_{oc} / I_{sc}

[Ω]

Norton Current

I_{N} = I_{sc} (s h or t - c i rc u i t c u rre n t)

[A]

Norton Resistance

R_{N} = R_{T h}

[Ω]

Max Power Transfer

P_{ma x} = \frac{V _{T h}^{2}}{4 R _{T h}}

maximum when R_L = R_{Th}

[W]

Chapter 6

Capacitors and Inductors

Study

Capacitor i-v

i = C \frac{d v}{d t}

[A]

Capacitor voltage

v = \frac{1}{C} \int i d t + v (0)

[V]

Capacitor energy

w = \frac{1}{2} C v^{2}

[J]

Series capacitors

1/ C_{e q} = 1/ C_{1} + 1/ C_{2} + \dots

[F]

Parallel capacitors

C_{e q} = C_{1} + C_{2} + \dots

[F]

Inductor v-i

v = L \frac{d i}{d t}

[V]

Inductor current

i = \frac{1}{L} \int v d t + i (0)

[A]

Inductor energy

w = \frac{1}{2} L i^{2}

[J]

Series inductors

L_{e q} = L_{1} + L_{2} + \dots

[H]

Parallel inductors

1/ L_{e q} = 1/ L_{1} + 1/ L_{2} + \dots

[H]

Chapter 7

First-Order Circuits

Study

RC Time Constant

τ = RC

[s]

RL Time Constant

τ = L / R

[s]

RC Natural Response

v (t) = V_{0} \cdot e^{- t / τ}

[V]

RL Natural Response

i (t) = I_{0} \cdot e^{- t / τ}

[A]

General 1st order

x (t) = x (\infty) + [x (0) - x (\infty)] e^{- t / τ}

[—]

Step Response RC

v (t) = V_{s} (1 - e^{- t / τ}) + V_{0} \cdote^{- t / τ}

[V]