# If a current of 4 A passing through a circuit generates 42 W of power, what is the resistance of the circuit?

Apr 24, 2016

$\approx 2.6 \Omega$

#### Explanation:

Power is current times voltage,

$P = I V$

Substituting in the power is $42 W$ and current is $4 A$ from the question,

$42 = 4 \cdot V$
$V = 10.5$

A second equation tells us that voltage is current times resistance, so

$V = I R$.

Putting in the values of $V = 10.5 V$ and $I = 4 A$ and rearranging to make $R$ the subject,

$R = \frac{10.5}{4} = 2.625 \Omega \approx 2.6 \Omega$

You could put the two equations together and say that

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

and simply solve straightaway.