Two resistors (both with R = 20.0 Ohm) and capacitor are connected to a 12.0 V b

Question

Two resistors (both with R = 20.0 Ohm) and capacitor are connected to a 12.0 V battery in a multi-loop RC circuit. A switch is closed at time t = 0 to begin charging the initially uncharged capacitor (C = 15.0 mu F). a. What is the initial value of the current flowing through each resistor at t = 0? b. What is the initial potential drop across each resistor at t = 0? c. What is the value of the current flowing through each resistor at t = infinity? d. What is the total charge stored on the capacitor at t = infinity?

Explanation / Answer

a) Initially the capacitor acts as short ckt.

so, I1 = V/R1 = 12/20 = 0.6 A

I2 = 0

b) at t = 0

potential across R1, V1 = I1*R1

= 0.6*20

= 12 volts

potential across R2, V2 = 0

c) After a long time the capacitor acts as open ckt.

so, I1 = I2 = V/(R1 + R2)

= 12/(20+20)

= 0.3 A

d) at t = infinite

voltage across capacitor, VC = voltage across R2

= I2*R2

= 0.3*20

= 6 volts

so, charge stored in the capacitor, Q = C*VC

= 15*6

= 90 micro C or 90*10^-6 C

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