# If a current of 4 A passing through a circuit generates 48 W of power, what is the resistance of the circuit?

Jan 3, 2016

$3 \Omega$

#### Explanation:

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

Where $P$ is power, $I$ is current, and $R$ is resistance.

Rearrange for $R$:

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

Substitute in values:

$R = \frac{48}{4} ^ 2$

$R = \frac{48}{16}$

$R = 3 \Omega$

Jan 3, 2016

$\Omega = 3 \text{ ohm}$

#### Explanation:

$P o w e r = \text{Voltage" * "Current}$
$\text{Resistance" = "Voltage"/"Current}$, so
$\text{Voltage"= "Resistance" * "Current}$, and
Power = ("Resistance" * "Current") * "Current"
$P o w e r = {\text{Resistance" * "Current}}^{2}$

In numbers:
$48 \text{W" = Omega * 4^2"A}$
$\frac{48}{16} = \Omega$
$\Omega = 3 \text{ ohm}$