# A charge of 36 C passes through a circuit every 9 s. If the circuit can generate 32 W of power, what is the circuit's resistance?

Feb 9, 2016

2 $\Omega$

#### Explanation:

We'll have to use a few formulas here. First, we will calculate the current of the circuit using the charge. Then, we will calculate the voltage using the power and current. The final calculation will involve using Ohm's Law to find resistance.

Current calculation:
Current, $I$, is defined as charge per second, or $\frac{C}{s}$. In this case, the charge is 36 coulombs and the time is 9 seconds, so current is $\frac{36}{9} = 4$ amps.

Voltage calculation:
Power is given by the formula $P = I E$. We have power and current, so we'll use them to find voltage. All we do is substitute: $32 = 4 E$, $E = 8$ volts.

Resistance calculation:
Finally, we can use Ohm's Law to find the resistance, $R$: $V = I R$.
$8 = 4 R$
$\frac{8}{4} = R$
$R = 2$ ohms

Thus the resistance is 2 $\Omega$.