What does this Circuit Analysis cheat sheet cover?

It has 10 sections: Basics, Series Parallel, Dividers, KCL KVL, Nodal Mesh, Sources Superposition, Thevenin Norton, C L Transients, AC Phasors and Op Amps. Together they cover the topics a typical Circuit Analysis exam tests, including Ohm's law and power, series and parallel, voltage and current dividers and KCL, KVL, nodal and mesh analysis.

Is the circuit analysis cheat sheet free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Circuit Analysis cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 3 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Circuit Analysis sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

Physics & EngineeringCircuit Analysis

Circuit Analysis Cheat Sheet — 1-page PDF

Core laws, methods, transients, phasors, op-amps. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

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For a specific exam: Circuit Analysis Final exam study sheet.

1 pageUS Letter
10 sections10 topics
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Preview of the one-page Circuit Analysis cheat sheet: Core laws, methods, transients, phasors, op-amps — the whole course, one page

On the sheet

What’s on it

The topics a typical Circuit Analysis exam tests, all on the one page.

Ohm's law and power
Series and parallel
Voltage and current dividers
KCL, KVL, nodal and mesh analysis
Thevenin and Norton equivalents
Superposition
Capacitors and inductors
First-order RC/RL transients
AC phasors and impedance
Op-amp configurations

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The free part, as text

The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01Basics

Current: $i (t) = \frac{d q}{d t}$ ; rate of flow of charge. Unit: ampere $A = C / s$ .
Voltage: $v_{ab} = v (a) - v (b)$ ; potential difference from node $b$ to node $a$ . Unit: volt $V$ .

Ohm

v = i R

Resistor, passive sign convention: current enters $+$ terminal.

Power

p = v i = i^{2} R = \frac{v ^{2}}{R}

Passive sign convention: $p > 0$ absorbed, $p < 0$ delivered.

Energy

w (t) = \int_{t_{0}}^{t} p (τ) d τ

Energy absorbed/delivered over time.

Element relations

Element	$v$ - $i$ law	Stored energy
$R$	$v = i R$	none
$C$	$i = C d v / d t$	$\frac{1}{2} C v^{2}$
$L$	$v = L d i / d t$	$\frac{1}{2} L i^{2}$

Watch out:Use the passive sign convention consistently; flipping current direction flips the sign of $p = v i$ .

02Series Parallel

Series resistors

R_{e q} = \sum_{k} R_{k}

Same current through each element.

03KCL KVL

KCL: At any node, algebraic sum of currents is zero: currents entering = currents leaving.
KVL: Around any closed loop, algebraic sum of voltages is zero.

KCL

\sum_{k} i_{k} = 0

Use signed currents at a node.

KVL

\sum_{k} v_{k} = 0

Use signed rises/drops around a loop.

Node/mesh choice

Method	Unknowns	Best for
Nodal	node voltages	many current sources
Mesh	loop currents	planar circuits with many voltage sources

Ex.Nodal at one node: resistor $R$ to ground, current source $I_{s}$ into node.

$\frac{v}{R} - I_{s} = 0 \Rightarrow v = I_{s} R$ .

Watch out:KVL is easiest in a single loop; for multiple meshes, define mesh currents and shared-element drops carefully.

04Nodal Mesh

Nodal equation

\sum_{k} \frac{v _{n} - v _{k}}{R _{nk}} = I_{n, inj}

At node $n$ ; use conductance form for resistors.

05Sources Superposition

Superposition

x = \sum_{k} x_{k}

In linear circuits, total response equals sum of responses to each independent source acting alone.

Turn off all other independent voltage sources: replace by short circuit.
Turn off all other independent current sources: replace by open circuit.
Keep dependent sources active.
Sum individual voltages/currents, not powers.

Watch out:Superposition applies to $v$ and $i$ , not directly to power: $p \neq = \sum p_{k}$ in general.

Ex.Find current due to two independent sources using superposition.

Solve circuit twice: source 1 active, source 2 off; then source 2 active, source 1 off. Add branch currents.

06Thevenin Norton

Thevenin equivalent: Any linear two-terminal network replaced by $V_{t h}$ in series with $R_{t h}$ .
Norton equivalent: Any linear two-terminal network replaced by $I_{N}$ in parallel with $R_{N}$ .

07C L Transients

Ex.RC: $v_{C} (0^{+}) = 2 V$ , $v_{C} (\infty) = 10 V$ , $τ = 3 ms$ . Find $v_{C} (t)$ .

$v_{C} (t) = 10 + (2 - 10) e^{- t /3 ms} = 10 - 8 e^{- t /3 ms}$ V.

08AC Phasors

Sinusoid: $x (t) = X_{m} cos (ω t + ϕ)$ or $X_{m} sin (ω t + ϕ)$ ; use one convention consistently.
Phasor: Complex amplitude representation of a sinusoid at angular frequency $ω$ .

Derivative/integral in phasors

\frac{d}{d t} \leftrightarrow j ω, \int d t \leftrightarrow \frac{1}{j ω}

Steady-state sinusoidal analysis.

Impedances

Z_{R} = R, Z_{L} = j ω L, Z_{C} = \frac{1}{j ω C}

Use in AC circuit equations.

Ohm in phasors

\underline{V} = \underline{I} Z

Underline denotes phasor; same circuit laws with complex numbers.

Admittance

Y = \frac{1}{Z}

Useful for parallel branches.

Phase behavior

Element	Current vs voltage
$R$	in phase
$L$	$i$ lags $v$ by $9 0^{\circ}$
$C$	$i$ leads $v$ by $9 0^{\circ}$

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Also on the full Circuit Analysis sheet

8 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

Series Parallel

Parallel resistors
Two in parallel
Series capacitors
Parallel capacitors
Series inductors
Parallel inductors

Dividers

Voltage divider
Two-resistor divider
Current divider
Two-branch current divider

Nodal Mesh

Ground reference
Mesh equation
Supermesh

Sources Superposition

Independent source
Dependent source

Thevenin Norton

Equivalence
Open-circuit voltage
Short-circuit current
Resistance by sources off

C L Transients

Capacitor
Inductor
Cap energy
Ind energy
RC time constant
RL time constant
First-order response

AC Phasors

Op Amps

Ideal op-amp
Golden rules
Inverting amplifier
Noninverting amplifier
Voltage follower
Summing amplifier
Integrator
Differentiator

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FAQ

Questions

About the Circuit Analysis sheet and making your own.

What does this Circuit Analysis cheat sheet cover?: It has 10 sections: Basics, Series Parallel, Dividers, KCL KVL, Nodal Mesh, Sources Superposition, Thevenin Norton, C L Transients, AC Phasors and Op Amps. Together they cover the topics a typical Circuit Analysis exam tests, including Ohm's law and power, series and parallel, voltage and current dividers and KCL, KVL, nodal and mesh analysis.
Is the circuit analysis cheat sheet free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Circuit Analysis cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 3 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Circuit Analysis sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

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