Electrical Power — Space Heater Current (Worked Example)

Easy

Problem

A 1500 W electric space heater plugs into a standard 120 V outlet. (a) What current does it draw? (b) What is the resistance of its heating element?

Given

P = 1500 W
V = 120 V

Find

Current I and resistance R.

Principle

Electrical power is the rate of energy transfer: P = VI. Combined with Ohm's law, resistance follows as R = V²/P.

Formula

I = \frac{P}{V}, \qquad R = \frac{V^2}{P}

I = P/V; R = V²/P

Solution

Current: $I = P/V = 1500/120$
Calculate: $I = 12.5\ \mathrm{A}$
Resistance: $R = V^2/P = 120^2/1500 = 14{,}400/1500$
Calculate: $R = 9.6\ \Omega$

I = 12.5 A; R = 9.6 Ω

Unit check

W/V = A; V²/W = V²/(V·A) = V/A = Ω. Both consistent.

What this means physically

12.5 A is near the 15 A limit of a typical household circuit — which is why two heaters on one circuit trip the breaker. The low 9.6 Ω resistance is deliberate: it lets a large current flow and dump 1500 J/s as heat.

Common mistake

Using R = V/I before finding I, then getting stuck — or mixing up P = VI with P = I²R and applying the wrong one to the knowns.