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) = (I_0)/(√(2))`
where
`I_0` is the peak value of the current. Substituting the second formula into the first one, we find

`P=( (I_0)/(√(2) ) )^2 R = (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{ (2 P)/(R) }= \sqrt{ (2 \cdot 2.0 W)/(47 \Omega) }=0.29 A`