Two resistors (Ri = 2.0 and R2-3.0 kQ) and two capacitors (Ci = 2.0 F and C2 = 3

Question

Two resistors (Ri = 2.0 and R2-3.0 kQ) and two capacitors (Ci = 2.0 F and C2 = 3.0 F) are hooked up to a battery with an EMF of = 120 V and a switch, as shown in the diagram. Assume that the ca- rs are initially uncharged and that the switch is initially open R2 C2 (5 points) What is the equivalent resistance and the equivalent capacitance of this comb nation of circuit components? a. b. (10 points) After the switch is closed, how long does it take for a total of 200. uC of charge to be stored on both capacitors? (5 points) How much charge is stored on each individual capacitor at the time you found in part 2b? c.

Explanation / Answer

(A) Req = R1 R2 / (R1 + R2)

Req = 1.2 kOhm

Ceq = C1 + C2 = 5 uF

(B) T = R C = 6 x 10^-3 s

and Q0 = 5uF x 120 = 600 uC

Q = Q0 [1 - e^(-t/T)]

200/600 = 1 - e(-t/T)

-t/T = ln(0.667 )

t =2.43 10^-3 s

(c) V = 200uc / 5uF = 40 Volt

Q1 = C1 V = 80 uF

Q2 = C2 V = 120 uF

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