Question

The average power dissipated in a 47 ω resistor is 2.0 w. what is the peak value i 0 of the ac current in the resistor?

Answer 1

The average dissipated power in a resistor in a ac circuit is:
$P=I_{rms}^2 R$
where R is the resistance, and $I_{rms}$ is the root mean square current, defined as
$I_{rms} = \frac{I_0}{\sqrt{2}}$
where $I_0$ is the peak value of the current. Substituting the second formula into the first one, we find
$P=( \frac{I_0}{\sqrt{2} } )^2 R = \frac{1}{2} I_0^2 R$
and if we re-arrange this formula and use the data of the problem, we can find the value of the peak current I0:
$I_0 = \sqrt{ \frac{2 P}{R} }= \sqrt{ \frac{2 \cdot 2.0 W}{47 \Omega} }=0.29 A$