The circuit in the figure below contains two resistors R1 22

The circuit in the figure below contains two resistors, R_1= 2.20 kH and R_2 = 3.50 kOmega, and two capacitors, C_1 = 2.30 MewF and C_2 = 3.10 MewF, connected to a battery with emf epsilon = 115 V. There are no charges on the capacitors before switch S is closed.

Solution

equivalent capacitance

C_eq =2.3+3.1 =5.4 uF

equivalent resistance

1/R_eq =1/2.2 + 1/3.5

R_eq=1.35 Kohms

Time Constant

T=R_eqC_eq =(1.35*10³)(5.4*10^-6)

T=7.29*10^-3 s

Voltage across capacitor in RC circuit as a function of time is given by

V=V_max[1-e^-t/T]

V=115[1-e^-t/0.00729]

a)

Charge across C1 is

Q₁=C₁V =(2.3u*115)[1-e^-137.2t]

Q₁=264.5[1-e^-137.2t] uC

b)

Charge across C2 is

Q₂=C₂V =(3.1u*115)[1-e^-137.2t]

Q₂=356.5[1-e^-137.2t] uC