# If a current of 8 A passing through a circuit generates 14 W of power, what is the resistance of the circuit?

Jan 13, 2016

The resistance in the circuit will be 0.22 $\Omega$

#### Explanation:

I would combine two laws I have memorised here: Ohm's Law,

$V = I R$

and the Power Law

$P = V I$

I have a current, $I$, of $\text{8 A}$ (ampere) and a power, $P$, of $\text{14 W}$ (watt). I have been asked for a resistance, $R$ $\Omega$ (ohm).

So I want a formula that includes only those three things. If I want to get rid of the $V$ in the Power Law, I can replace it with what Ohm's Law says is equal to $V = I R$. So

$P = \left(I R\right) \cdot I = {I}^{2} \cdot R$

I need to rearrange to make $R$ the subject, so I divide both sides by ${I}^{2}$ and swap the sides:

$R = \frac{P}{{I}^{2}} = \frac{14}{{8}^{2}} = \frac{14}{64} = 0.22 \textcolor{w h i t e}{a} \Omega$ (rounded to two decimal places).