a Find the source voltage b Determine the two times after t0

a) Find the source voltage.
b) Determine the two times after t=0 when the power out of the voltage source is zero.

In the circuit shown in Fig. P3.12, the initial voltage on the capacitor is 10 V, with the + at the bottom, and the initial current in the inductor is zero. The current into the capacitor is S A de for t> 0, as shown. (a) Find the source voltage. (b) Determine the two times after t = 0 when the power out of the voltage source is zero. 5 A R= 1 Figure P3.12

Solution

a) first find Voltage of inductor
=v(0) + S i(t) dt
=10 + -5t
use kvl to find Vs   remember that polarity ofcapacitor is unconventional
yields Vs(t)=5t-10
b) two times that Power out of Vs=0
Power out = V*I
shortcut is to determine when I=0 and when V=0
Vs(t)=0=5t-10   ie 5t=10 t=2
other solution I believe neglected rules for repeatedroots
second time can be calculated by finding when the inductor andresistor currents negate capacitor current
IofR+IofL=-5
yields 1/2x^2 -x -1 = 0
t2=1+sqrt(3)