# How much power is produced if a voltage of 4 V is applied to a circuit with a resistance of 27 Omega?

Feb 18, 2016

Combining $P = V I$ and $V = I R$ (Ohm's Law) yields $P = {V}^{2} / R = {4}^{2} / 27 = \frac{16}{27} \approx 0.59$ $W$

#### Explanation:

Probably not a lot more explanation needed. We are given a voltage $\left(V\right)$ and a resistance $\left(\Omega\right)$. We know that the expression for power in a circuit is $P = V I$, but we don't know the current.

We do know a way to find the current, given the voltage and the resistance: Ohm's Law :

$V = I R$

Rearranging:

$I = \frac{V}{R}$

We could calculate the current and then substitute that into the expression for the power, but I decided to combine the equations instead:

$P = V I = V \left(\frac{V}{R}\right) = {V}^{2} / R$

Then it's just a matter of substituting in the values we have and we know the power produced by the circuit.