Chapter 5.7, Problem 9E

To determine

(a)

To show:

The steady state solution is $q_p\left(t\right)=\frac{E_0}{1/C-{\gamma }^{2}L+i\gamma R}{e}^{i\gamma t}$.

To determine

(b)

To show:

The steady state solution current is $I_p\left(t\right)=\frac{E_O}{R+i\left[\gamma L-\frac{1}{\left(\gamma C\right)}\right]}{e}^{i\gamma t}$

To determine

(c)

To show:

The steady state solution current is $I_p\left(t\right)=\frac{E_O{e}^{i\left(\gamma t+\theta \right)}}{\sqrt{R^2+{\left[\gamma L-\frac{1}{\left(\gamma C\right)}\right]}^2}}$

To determine

(d)

To verify:

The imaginary part of $I_p$ is $\frac{E_O\sin \left(\gamma t+\theta \right)}{\sqrt{R^2+{\left[\gamma L-\frac{1}{\left(\gamma C\right)}\right]}^2}}$.