Answer
Energy is delivered to the box by the generator at an average rate of $~~33.4~W$
Work Step by Step
We can find the impedance $Z$:
$Z = \frac{\mathscr{E}_m}{I} = \frac{75.0~V}{1.20~A} = 62.5~\Omega$
We can find $R$:
$Z = \sqrt{R^2+R^2~tan^2~\phi}$
$Z = \sqrt{R^2(1+tan^2~\phi)}$
$Z^2 = R^2(1+tan^2~\phi)$
$R^2 = \frac{Z^2}{1+tan^2~\phi}$
$R = \sqrt{\frac{Z^2}{1+tan^2~\phi}}$
$R = \sqrt{\frac{(62.5~\Omega)^2}{1+tan^2~(-42.0^{\circ})}}$
$R = 46.45~\Omega$
We can find the average power:
$P_{ave} = I_{rms}^2~R$
$P_{ave} = (\frac{I}{\sqrt{2}})^2~(R)$
$P_{ave} = (\frac{1.20~A}{\sqrt{2}})^2~(46.45~\Omega)$
$P_{ave} = 33.4~W$
Energy is delivered to the box by the generator at an average rate of $~~33.4~W$
