Chapter 31, Problem 73E

(a)

To determine

To show: The instantaneous power into the resistor is $p_R=V_{R}I{\cos }^2\omega t$ and $p_R=\frac{1}{2}{V}_{R}I\left(1+\cos \left(2\omega t\right)\right)$ and determine the expression for average power into the resistor.

(b)

To determine

To show: The instantaneous power into the inductor is $p_L=-V_{L}I\sin \omega t\cos \omega t$ and $p_L=-\frac{1}{2}{V}_{L}I\sin \left(2\omega t\right)$ and determine the expression for average power into the inductor.

(c)

To determine

To show: The instantaneous power into the capacitor is $p_C=V_{C}I\sin \omega t\cos \omega t$ and $p_C=\frac{1}{2}{V}_{C}I\sin \left(2\omega t\right)$ and determine the expression for average power into the capacitor.

(d)

To determine

To show: At each instant of time $p_R+p_L+p_C=VI\cos \omega t\left(\cos \varphi \cos \omega t-\sin \varphi \sin \omega t\right)$.