# If a current of 6 A passing through a circuit generates 12 W of power, what is the resistance of the circuit?

$\frac{1}{3} \setminus \setminus \Omega$

#### Explanation:

Power ($P$) of a circuit carrying a current $I$ & having a resistance $R$ is given as
$P = {I}^{2} R$
but given that $I = 6 A$ & power $P = 12 W$ hence
$12 = {6}^{2} R$
$R = \setminus \frac{12}{36}$
$R = \frac{1}{3} \setminus \setminus \Omega$

Jun 20, 2018

Approximately $0.33$ ohms.

#### Explanation:

Power is related through resistance and current by the equation:

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

where:

• $P$ is the power in watts

• $I$ is the current in amperes

• $R$ is the resistance in ohms

Rearranging for resistance, we get:

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

Now, plugging in our given values, we find that:

$R = {\left(12 \setminus \text{W")/(6 \ "A}\right)}^{2}$

$= \left(12 \setminus {\text{W")/(36 \ "A}}^{2}\right)$

$= \frac{1}{3} \setminus \Omega$

$\approx 0.33 \setminus \Omega$