The circuit In the figure below contains two resistors, R_1 = 1.50 kohm and R_2

Question

The circuit In the figure below contains two resistors, R_1 = 1.50 kohm and R_2 = 2.50 kohm, and two capacitors, C_1 = 2.10 muF and C_1 = 2.10 muF, and c_2 = 2.60 muF, connected to a battery with emf epsilon = 115 V. There are no charges on the capacitors before switch S Is closed. (a) Determine the charge on capacitor C_1 as a function of time (in ms), after the switch is closed.(Use the following as necessary: t,) q_1 = muC (b) Determine the charge on capacitor c_2 as a function of time (in ms), after the switch is closed.(use the following as necessary: t.) q_2 = muC

Explanation / Answer

Here,

for the capacitors and resistors

Req = R1 || R2

Req = 1.5 * 2.5/(1.5 ( 2.5))

Req = 0.94 kOhm

Ceq = 2.5 + 2.1

Ceq = 4.6 *10^-6 F

T = Ceq * Req

T = 0.94 *10^3 * 4.6 *10^-6

T = 4.324 *10^-3 s

T = 4.324 ms

Now , the voltage across the capacitors is given as

V = E * (1 - e^(-t/T))

V = 115 * (1 - e^(-t/4.324))

a) charge across C1

charge across C1 = C1 * V

charge across C1 = 115 * (1 - e^(-t/4.324)) * 2.10

charge across C1 = 241.5 (1 - e^(-t/4.324)) uC

b)

charge across C2 = 115 * (1 - e^(-t/4.324)) * 2.60

charge across C2 = 299 * (1 - e^(-t/4.324)) uC

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