EP 229 Assignment 10 (due Tuesday April 5)
1. In capacitor discharging through an RL series circuit, the energy decreases by 1 % in each
oscillation when R = 2 : If the resistance is removed, the LC circuit oscillates at f = 1 kHz.
Find the values of L and C: The circuit is weakly damped and the capacitor charge may be
approximated by
0s
1
q (t) = q0 exp
Ans. L = 0:199 H, C = 127 nF.
R
t cos @
2L
2. Find the current when the voltage across a 50
1
LC
R
2L
2
tA
inductive reactance is given as follows:
(a) 50 sin !t
(b) 30 sin (!t + 20 )
(c)
80 sin (377t + 40 )
3. Repeat 2 for a
30
capacitive reactance.
4. Problem 33.25.
5. Problem 33.39.
6. A series LCR circuit is driven by an oscillating voltage source v (t) = 6 sin (314t + 60 ) : The
resistance of the circuit is 3 k ; the inductive reactance is 2 k and capacitive reactance is
1 k :Find
(a) the total impedance
(b) the RMS current
(c) the average power dissipated in the resistor
Ans. Z = 3:166 18:4
; iRM S = 1:34 mA, Pave = 5.4 mW.
7. Find the total impedance seen by the 15 V (RMS) voltage source, the RMS current driven
and the average power delivered by the voltage source.
3.5 µF
15 V
500 Hz
Ans. Z = 99:86
10 µF 20 Ohms
30 mH 15 mH
60:6 ; 1.1 W.
1
30 Ohms