Ohm's Law, Series vs Parallel Resistors

Ohm's Law, Series vs Parallel Circuits and Equivalent Resistance

By StudyStore · Published 2026-11-05 · 1 min read · 194 words

Ohm's law: V = IR. Power: P = IV = I²R = V²/R.

Series vs parallel

	Series	Parallel
Equivalent resistance	R = R₁ + R₂ + ...	1/R = 1/R₁ + 1/R₂ + ...
Current	Same through each	Splits; sums to total
Voltage	Splits; sums to total	Same across each
Adding a resistor	R goes up	R goes down

Parallel equivalent resistance is always smaller than the smallest branch.

Worked example

A 12 V battery drives a 4 ohm and a 12 ohm resistor in parallel. R = (4 x 12)/(4 + 12) = 3 ohm. Total current = 12 / 3 = 4 A. Branch currents: 12/4 = 3 A and 12/12 = 1 A, which sum to 4 A.

Capacitors flip the rule

Capacitors in parallel add; in series they combine like resistors in parallel.

Common traps

Adding parallel resistors directly. Use reciprocals.
Assuming current is the same in parallel. Voltage is the same.
Ignoring internal resistance of the battery when a question gives it.

One-minute recap

V = IR.
Series: same I, add R. Parallel: same V, add 1/R.
Parallel lowers total R.

Check yourself: 5-question mini-quiz

Try each question first, then click it to reveal the answer.

1. What is the equivalent resistance of 4 ohm and 12 ohm in parallel?

3 ohm.

2. What stays the same across parallel branches?

Voltage.

3. What happens to total resistance when a resistor is added in series?

It increases.

4. Write one expression for power.

P = IV, I^2 R or V^2 / R.

5. How do capacitors in parallel combine?

Their capacitances add.

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Written by StudyStore from standard scientific facts. Study aid only. Always check values against the reference your exam provides.