3 · Resistance and Ohm's Law

What resistance is

Picture a hose. Squeeze it narrower, and less water gets through for the same pump pressure. A resistor does the same thing to charge — it makes the path harder to push charge through, so for the same battery push (EMF), a bigger resistance means less current.

Resistance is measured in ohms (Ω). One ohm means one volt of push is needed to drive one amp of current through it: 1 Ω = 1 V / 1 A.

Ohm's Law

Ohm's Law ties voltage, current and resistance together in one formula:

V = I × R

You'll need to rearrange this constantly, so it's worth knowing all three forms cold:

I = V / R · R = V / I

Worked example — finding current

A 12 V battery is connected to a 4 Ω resistor. What current flows?

I = V / R = 12 ÷ 4 = 3 A

Worked example — finding resistance

A resistor has 2 A flowing through it when connected to a 9 V supply. What is its resistance?

R = V / I = 9 ÷ 2 = 4.5 Ω

Notice Keep the battery push fixed and drag only the resistance slider up. The current reading falls — and it falls by the same factor the resistance rose by. Double R, and I halves. That's the inverse relationship Ohm's Law describes.

Quick check

Q A lamp has resistance 6 Ω. A current of 1.5 A flows through it. What is the p.d. across the lamp?

V = I × R = 1.5 × 6 = 9 V