# A charge of 18 C passes through a circuit every 24 s. If the circuit can generate 8 W of power, what is the circuit's resistance?

May 29, 2016

$R = 14.22 \text{ } \Omega$

#### Explanation:

$\Delta Q = 18 C \text{ charge passing through circuit}$
$\Delta t = 24 s \text{ time}$
$P = 8 W \text{ power generated by circuit}$
R=?

$\text{current is described as } I = \frac{\Delta Q}{\Delta t}$

$I = \frac{18}{24} = \frac{3}{4} A$

$\text{remember that } P = {I}^{2} \cdot R$

$8 = {\left(\frac{3}{4}\right)}^{2} \cdot R$

$8 = \frac{9}{16} \cdot R$

$R = \frac{8 \cdot 16}{9}$

$R = 14.22 \text{ } \Omega$