# Power in DC Circuits

fact

Power is a measure of how much energy is given off or used up by an element in a circuit every second.

fact

Power is measured in Joules per Second and uses the unit Watt (denoted W)

law

Power is simply the voltage across an element multiplied by the current through it:
\(P = VI\)

example

Find the power across the resistor below.

From the circuit we can see that the voltage across the resistor \(V_r = 10\)V and from Ohm's Law we know the current is \(I_r = 100\)mA. So the power absorbed by the resistor is \(P_r = V_r\times I_r = 1\)W.fact

We can rearrange our basic power formula: \(P = VI\) using Ohm's Law to get a few other forms.
By using \(I = \frac{V}{R}\) we get: \(P = \frac{V^2}{R}\)
By using \(V = IR\) we get: \(P = I^2 R\)

example

Find the resistance of resistor R in the diagram below

We have voltage and power and we need resistance so, looking through our formulas, I'm going to pick the one that only uses voltage, power and resistance. \(P = \frac{V^2}{R}\) Now we'll plug in the values we have: \(1.4 = \frac{100}{R}\) Rearrange to solve for \(R\) and we get: \(R = \frac{100}{1.4} = 71.43\)
practice problems