Chapter 31, Problem 56E

(a)

To determine

To Prove: The instantaneous voltage at any instant is equal to $v$ and the total current $i$ equal to the sum of the currents flowing through the resistor, capacitor and inductor.

(b)

To determine

The phases of $i_R$, $i_L$ and $i_C$ with respect to $v$ and also to draw the phasor diagram using the current phasors.

(c)

To determine

To Prove: The current amplitude $\left(I\right)$ for the instantaneous current $\left(i\right)$ through the source is $I=\sqrt{I_R^2+{\left(I_C-I_L\right)}^2}$.

(d)

To determine

To show: The result from part (c) can be written as $\frac{1}{Z}=\sqrt{{\left(\frac{1}{R}\right)}^2+{\left(\omega C-\frac{1}{\omega L}\right)}^2}$.