# If a current of 5 A passing through a circuit generates 450 W of power, what is the resistance of the circuit?

Jan 18, 2016

Electrical power is given by $P = {I}^{2} R$. Rearranging to make resistance the subject, $R = \frac{P}{I} ^ 2 = \frac{450}{5} ^ 2 = 18 \Omega$

#### Explanation:

Different people learn differently. Some memorize all the possible formulae. That works, but my approach is to memorize as few as possible and understand them well enough to combine them.

Summarising the data:
$P = 450 W$
$I = 5 A$
R=? Omega

I remember Ohm's Law: $V = I R$ and I remember that for power, $P = V I$. I don't have a voltage in my data summary, so I can't use $P = V I$ directly, but if I substitute in $I R$, which Ohm's Law tells me is equal to $V$, I get $P = I R \cdot I = {I}^{2} R$.

Now I just need to rearrange to make $R$, the unknown thing, the subject (left side) of the equation:

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

Then substitute in the data:

$R = \frac{P}{I} ^ 2 = \frac{450}{5} ^ 2 = 18 \Omega$