Question

A 120 V fish-tank heater is rated at 130W. Calculate (a) the current through the heater when it is operating, and (b) its resistance

Answer 1

Explanation:

The power P dissipated by a heater is defined as

$P = VI$

where V is the voltage and I is the current.

a) The current running through a 130-W heater is

$I = \dfrac{P}{V} = \dfrac{130\:\text{W}}{120\:\text{V}} = 1.08\:\text{A}$

b) The resistance R of the heater is

$P = VI = (IR)I = I^2R$

where $V= IR$ is our familiar Ohm's Law.

$\Rightarrow R = \dfrac{P}{I^2} = \dfrac{130\:\text{W}}{(1.08\:\text{A})^2}$

$R = 110.8\:Ω$