1. The circuit shown includes a switch that is connected initially (for t<0) to
ID: 1812006 • Letter: 1
Question
1. The circuit shown includes a switch that is connected initially (for t<0) to the 4V voltage source. At t=0, the switch changes state so that the 4V source is replaced with a 0 volt source ( a wire). Assuming the circuit was in steady state before the switch changed state, find the value of the voltage Vc(0-), i.e. the voltage across the capacitor in steady state in the old circuit.
2.For the circuit of problem 1, find the current through the capacitor (flowing in the downward direction) at time (0-). Once again 0- indicates the steady state of the old circuit.
3.For the circuit of problem 1, find the current through the capacitor at time (0+).
(Hint: The current through a capacitor does not have to be continuous. Using the fact that Vc(0-)=Vc(0+), replace the capacitor with a voltage source equal to Vc(0-), combine the resistors that can be combined and write a KVL equation to solve for the current).
Explanation / Answer
1. Vc(0-)=2V...Capacitor behaves as an opne ckt Vc(0-)=voltage acroos 2 ohm resistor.........2. .I=0 at steady state ..its an open ckt ........3.), replace the capacitor with a voltage source equal to Vc(0-), combine the resistors that can be combined and write a KVL equation to solve for the current Req will become 1+2||(2).......hence effective resistance will be 2 ohm ,,,,,q/c + dq/dt =0 ..solving we will get .....i=q(0)/R*C *exp(-t/RC) ..putting the value we get i= 1A
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