# A charge of 18 C passes through a circuit every 6 s. If the circuit can generate 24 W of power, what is the circuit's resistance?

Mar 18, 2016

$R = 2.67 \Omega$

#### Explanation:

Let's start by thinking about what we know and what we want to find out. We know the power generated by the circuit, and we know the current, since current is charge per unit time:

$I = \frac{Q}{t} = \frac{18 C}{6 s} = 3 A$

And we wish to know the resistance. We know the equation for the power generated by a circuit in Joule's Law which states:

$P = V \cdot I$

And we know the relationship between current, voltage and resistance from Ohm's Law which states:

$V = I \cdot R$

If we substitute $I \cdot R$ for $V$ into Joule's Law we get

$P = {I}^{2} R$

Which we can solve for $R$

$R = \frac{P}{{I}^{2}} = \frac{24 W}{3 A} ^ 2 = 2.67 \Omega$