# If a current of 4 A passing through a circuit generates 16 W of power, what is the resistance of the circuit?

Feb 9, 2016

1 $\Omega$

#### Explanation:

We will be using two formulas: the one for power, to calculate voltage, and Ohm's Law, to calculate resistance.

Power is given by: $P = I E$, where $I$ is the current and $E$ is the voltage. We are given the power (16 watts), and the current (4 amps), and we can use these to get the voltage:
$16 = 4 E$
$\frac{16}{4} = E$
$E = 4$ volts

Now we use Ohm's Law, which states that $V = I R$, where $V$ is the voltage, $I$ is current, and $R$ is resistance. We have the voltage (4 volts) and current (4 amps), so all we do is substitute:
$4 = 4 R$
$\frac{4}{4} = R$
$R = 1$ ohm

Therefore, the resistance is 1 $\Omega$.