If someone could please help me with this question that\'d be great! Thank you!

Question

If someone could please help me with this question that'd be great! Thank you!

C = 5 times 10^-3 F R = 2000 ohms Initially, the switch S is open and the capacitors are uncharged a) What is the equivalent capacitance of the capacitors in the above circuit? b) If the switch S is closed, what is the time constant of the RC circuit? c) What is the final total charge (Q_0) stored on the capacitors? d) What is the charge stored on the equivalent capacitor after 2 seconds e) What is the time taken for the capacitors to be charged 70% (Q/Q_0 = 0.7)

Explanation / Answer

Here ,

a) for the equivalent capacitance

1/Cnet = 1/(3C) + 1/C + 1/C + 1/C

1/Cnet = 1/0.30C

Cnet = 0.30C

Cnet = 0.30 * 5 *10^-3 = 1.5 *10^-3 F

b)

time constant = R * Cnet

time constant = 2000 * 1.5 *10^-3

time constant = 3 s

c)

final total charge = 1.5 *10^-3 * 20 = 0.03 C

d)

after 2 s

Q = 0.03 * (1 - e^(-t/T))

Q = 0.03 * (1 - e^(-2/3))

Q = 0.0146 C

the charge is 0.0146 C

e)

let the time taken is t

Q = Qo * (1 - e^(-t/T))

0.70 = 1 - e^(-t/3)

solving for t

t = 3.61 s

the time taken is 3.61 s

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