UTAH STATE UNIVERSITY
ELECTRICAL and COMPUTER ENGINEERING DEPARTMENT

ECE 3620 Sept. 12, 2008

Homework: # 4

Due Sept. 19, 2008

For each problem, you must show your work!

1. (NR Prob 8.3) For a parallel RLC circuit, the natural voltage response is measured to be
   
   $$v(t) = 125 e^{-4000 t}(\cos 3000 t - 2 \sin 3000 t) \qquad t \geq 0$$
   
   
   when $C=50 nF$. Determine $L$, $R$, $v_c(0)$, $i_L(0)$, and $i_L(t)$.
2. For a series RLC circuit, show that the roots of the characteristic equation are
   
   $$s_1 = -\alpha + \sqrt{\alpha^2 - \omega_0^2} \qquad s_2 = -\alpha - \sqrt{\alpha^2 - \omega_0^2}$$
   
   
   where
   
   $$\alpha = \frac{R}{2L} \qquad \omega_0^2 = \frac{1}{LC}$$
   
   

3. Problem 9.74 in NR (Handout on web)

4. 13.1-1
5. 13.2-1
6. 13.2-2
7. 2.2-1
8. 2.2-2
9. 2.2-3
10. 2.2-4
11. 2.2-7