Question

The below are initially uncharged. (a) What is the time constant for charging the capacitors? (b) How much time is required for the capacitors to reach 50% of their full charge? (c) What is the maximum charge on the capacitors? (d) When the switch is initially closed, what the in each of the resistors? (e) When the is what are the currents (e) 50% charged 30 2 20 V 40 uF 60 uF 45

If capacitors and resistors can be arranged are the resistors in series? Then is the final current on the resistors .135 Amps?

Answer 1

Lets first find the equivalent capacutance and resistance

Ceq = C1 + C2 = 40 + 60 = 100 uF

Req = R1 + R2 = 30 + 45 = 75 Ohm

a)Time constant in RC is:

t = RC

t = 75 x 100 x 10^-6 = 7.5 x 10^-3 s = 7.5 ms

Hence, t = 7.5 ms

b)we know,

Q = Qm (1 - e^-t/RC)

0.5 Q = Q (1 - e^-t/RC)

0.5 = (1 - e^-t/RC)

e^-t/RC = 0.5

taking natural log both sides,

-t/RC = -0.693

t = 0.693 x RC = 0.693 x 75 x 100 x 10^-6 = 0.0052 s

Hence, t = 0.0052 s = 5.2 ms

C)Qmax = CV

Qmax = 100 x 10^-6 x 20 = 2000 x 10^-6 C

Hence, Q max = 2 x 10^-3 C = 2 mC

D)I = V/R = 20/75 = 0.27 A

Hence, I = 0.27 A