Okay this is a 'basic' transient question but I'm not sure what to do for 8.3 and 8.4

QUESTION 8 [4 MARKS]
A 1F capacitor is connected in series with a 1Ω resistor across a 10V DC supply. A switch is also connected in series with another 1Ω resistor, which is connected in parallel with the capacitor.

Initially, the switch is open, however at t=0 the switch is closed.
8.1. Find the initial steady state voltage across the capacitor before the switch is closed. [1]

I got this to be 10V ???

8.2. Find the final steady state voltage across the capacitor once the switch is closed. [1]

I got 5V ???

8.3. How much time would have to pass once the switch is closed, for the voltage to reach 136.8% of it’s
final value. [1]

How would I go about doing this and 8.4?

8.4. How much energy is retained in the capacitor at this time? [1]

 

You are right about 8.1 and 8.2.

For 8.3, fins the time it needs to drop from the initial 10V to 6.84V (136.8% of 5V) after the switch closes.

For 8.4, use E=0.5*C*V^2

 

8.4 i guess is just (1/2)CV^2

I thought of doing 8.3 as 5(1.368) = 10(1 - e^(-T/RC)
RC =1
T = 1.15 seconds but this doesn't seem to be correct somehow?

 

never refreshed to see your reply before i posted, is my way of doing 8.3 correct?...

 

Because you have an initial charge on the capacitor you have to use this formula:

Vc=Vfinal(1-exp(-t/RC)+Vinitial*exp(-t/RC)

 

I have just looked at the provided solution and it says 1.15 seconds, the way you provided seems to get me 0.999.... Am not sure which one is correct... Or maybe I have misunderstood your formula

 

When the switch is closed the time constant is not 1 but 0.5 because the resistance seen by the capacitor is the parallel combination of the two 1R resistors.

 

according to a computer simulation, the time taken is 0,5 seconds. I reworked RC to be 0.5, and I don't get the 0.5 seconds as the answer though??

 

according to a computer simulation, the time taken is 0,5 seconds. I reworked RC to be 0.5, and I don't get the 0.5 seconds as the answer though??

I get 0.5 sec.

 

Mik3 is quite correct.

Sometimes it helps to draw pictures and write things down together ....