Electricity — Cheat Sheet

OHM'S LAW + BASIC QUANTITIES

Charge & Current

Q = It

Coulombs; I in A, t in s

Conventional

current: + → −

Ohm's Law — V = IR

V = IR

find voltage

I = V/R

find current

R = V/I

find resistance

Units: V = Volts · I = Amperes (Amps) · R = Ohms (Ω)

Ohmic device: V-I graph is a straight line through the origin. Slope = R.

DC vs AC

one direction only — battery

reverses direction — household outlet

SERIES vs PARALLEL

Series

Current

I same everywhere

Rₜ

R₁ + R₂ + R₃

Vₜ

V₁ + V₂ + V₃

V ratio

V₁/V₂ = R₁/R₂

Parallel

Voltage

V same across each branch

1/Rₜ

1/R₁ + 1/R₂ + 1/R₃

Two R shortcut

R₁R₂/(R₁+R₂)

Iₜ

I₁ + I₂ + I₃

Key: Rₜ parallel is always < smallest branch R

MIXED CIRCUITS

Simplify parallel groups first
Then add series resistances
Find total I, then work back

POWER & ENERGY

Power — 3 forms (pick based on knowns)

P = VI

when V and I both known

P = I²R

when I and R known (series)

P = V²/R

when V and R known (parallel)

Energy

E = Pt = VIt

Joules

1 kWh

3.6 × 10⁶ J

Cost

(P in kW) × (h) × ($/kWh)

Tip: 60 W bulb for 4 h = 0.06 kW × 4 h = 0.24 kWh

QUICK WORKED EXAMPLE

Series: R₁=10Ω, R₂=15Ω, V=50V
Rₜ=25Ω · I=2A
P₁=I²R₁=40W · P₂=I²R₂=60W
Pₜ=VI=100W ✓

MAGNETISM

Magnetic force formulas

On a charge

F = qvB sinθ

On a wire

F = BIL sinθ

angle between v (or I) and B

Right-hand rules

Straight wire: thumb = current → fingers curl = B direction
Force on wire: fingers = I, curl toward B → thumb = force
Force is always ⊥ to both v and B
Parallel to B (θ=0°) → F = 0

COMMON MISTAKES

Mistake	Remember instead
Series: current splits	Current same, voltage splits
Parallel: voltage splits	Voltage same, current splits
Parallel Rₜ > branches	Always less than smallest R
P=I²R in parallel	Use P=V²/R (same V)
P=V²/R in series	Use P=I²R (same I)
Mag. force along motion	Always ⊥ — changes direction, not speed