UTAH STATE UNIVERSITY
ELECTRICAL and COMPUTER ENGINEERING DEPARTMENT

ECE 3620 Sept. 5, 2008

Homework: # 3

Due Sept. 12, 2008

For each problem, you must show your work!

1. 1.4-8
2. 1.4-9
3. 1.5-1(a,c,d,e,f)
4. 1.7-1(a,b,c,g)
5. 1.7-2(a,b,d,e,f)
6. 1.7-4
7. 1.8-2
8. (NR drill 8.1): A parallel RLC circuit has $L=20 mH$ and $R = 100 \Omega$.
   1. Find the value of $C$ that makes the voltage response critically damped.
   2. Find the value of $C$ that gives a neper frequency of 5000 rad/sec; for this value of $C$ determine the roots of the characteristic equation.
   3. Find the value of $C$ that gives a resonant frequency of $\omega_0 = 20$ krad/sec, and determine the roots of the characteristic equation.

9. (NR Drill 8.2) For a parallel RLC circuit with $C=0.2 \mu F$, $L=50 mH$, and $R = 200 \Omega$, having an initial capacitor voltage $v_0(0) = 12$ V and an initial inductor current $i_L(0) = 30 mA$, determine an expression for $i_L(t)$. Hint: find $v(t)$, then use the integral relationship between $i_L$ and $v_R$.