Please answer this question and all parts. Show all work. Thanks. 8. Consider th

Question

Please answer this question and all parts. Show all work. Thanks.

8. Consider the following RC circuit. The capacitor is initially uncharged. a) At 0 the switch S is thrown to point a in the circuit shown. Apply Kirchhoff's Loo to the circuit and write an equation for the circuit at any time t. (Use q as the instantaneous charge on the capacitor, and i as the instantaneous current in the circuit at time t) b) What is the charge on the capacitor when the instantaneous current in the circuit is 2.0 mA, with 2 LIF switch S still at position a? e switch stays connect switch s is thrown to b. At what time does the charge on the capacitor become 20.0uC?

Explanation / Answer

A)

For the circuit, using Kirchoff loop rule:

30=i*R + C*dV/dt

Here: R = 7k ohm

C = 2 uF

V = (30 - iR)

So, 30 = i*R + C*d(30 - i*R)/dt

So, 30 = iR - CR*di/dt

B)

Charge on the capacitor is given by:

Q = Qo*e^(-t/RC)

And current,  

I = Io*e^(-t/RC)

So, 2 = (30/7)*e^(-t/(7*0.002))

So, t = 0.0107 s

So, Q = 60*10^-6*14/30

= 2.8*10^-5 C

C)  

20 = 28*e^(-t/(7000*2*10^-6))

So, t = 4.71 ms

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