# A charge of 15 C passes through a circuit every 12 s. If the circuit can generate 18 W of power, what is the circuit's resistance?

Mar 3, 2016

The resistance is $11.52$ $\Omega$

#### Explanation:

First, let's think about what we are trying to calculate. We know the power generated from the circuit which is given by Joule's law:

$P = I \cdot V = 18$ $W$

We have also been given the rate of charge flow, which is a current:

$I = \frac{Q}{t} = \frac{15 C}{12 s} = 1.25$ $A$

We can substitute this current into the first equation and solve for the voltage:

$V = \frac{18 W}{1.25 A} = 14.4$ $V$

Now we have a current and a voltage and want to find a resistance. We know Ohm's Law relates all three of these:

$V = I \cdot R$

Rearranging to find the resistance:

$R = \frac{V}{I} = \frac{14.4 V}{1.25 A} = 11.52$ $\Omega$