Electricity & magnetism · Topic 15 of 17

Current, Voltage, Resistance & Ohm's Law

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Physics · circuits

Voltage pushes current through resistance, V = IR; series parts share one current, parallel branches share one voltage, and power is P = IV.

01 · Ohm's lawV = I × R

02 · ParallelParallel: 1/R = 1/R1 + 1/R2 + …

03 · PowerP = I × V (watts)

Current in amperes (A), voltage in volts (V), resistance in ohms (Ω) must know

Voltage = energy per charge; 1 V = 1 J/C

Current needs a closed loop; a break anywhere stops it

Longer, thinner, or hotter metal wire → more resistance

Household wiring is parallel: full voltage to each device

Series: same current through all; R = R₁ + R₂ + … must know

Parallel: same voltage on each; 1/R = 1/R₁ + 1/R₂; total < smallest must know

Conventional current runs + to −; electrons move the opposite way

Ohm's law: V = IR (so I = V/R and R = V/I) must know

Power P = IV, in watts (also P = I²R = V²/R) must know

I = Q/t; 1 A = 1 coulomb per second

120 V, 0.50 A → R = 240 Ω, P = 60 W

4 + 6 + 10 Ω in series on 12 V → 20 Ω, 0.60 A

6 Ω ∥ 3 Ω on 12 V → 2 Ω, 6 A total (2 A + 4 A)

Series: one break stops all; parallel branches work independently

Commonly confused

	Series	Parallel
Current	Same through every part	Splits; branch currents add to the total
Voltage	Divides; drops add up to the source	Full source voltage on each branch
Total resistance	R = R₁ + R₂ + … (bigger than any one)	1/R = 1/R₁ + 1/R₂ + … (less than the smallest)
One part breaks	Whole circuit stops	Other branches keep working
6 Ω with 3 Ω	9 Ω	2 Ω

Trap: adding in parallel lowers total R; adding in series raises it

Show 4 more facts

E = Pt; 1 kWh = 3.6 × 10⁶ J

R = ρL/A (resistivity × length ÷ area)

Two in parallel: R = R₁R₂/(R₁ + R₂); two equal → half

Ohm's law holds for ohmic materials, not every device

Pearl

Series shares the current; parallel shares the voltage.

Practice this topic, then test the whole section.

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