The diagram below depicts an RC -circuit where C 1 = 6.55 ?F, C 2 = 2.45 ?F, R 1

Question

The diagram below depicts an RC-circuit where C1 = 6.55 ?F, C2 = 2.45 ?F, R1 = 22.5 ?, R2 = 23.5 ?, and ?1 = 6.00 Volts.

1. What is the final amount of charge stored in C2?
(in C)

2. What is the amount of charge stored in C1 after the switch S has been closed for t = 5.00E-6 seconds?
(in C)

3. What is the initial current through the circuit immediately after the switch S is closed?
(in A)

4. What is the current through the circuit after the switch S has been closed for t = 5.00E-6 seconds?
(in A)

A: 2.57×10-6 B: 3.42×10-6 C: 4.55×10-6 D: 6.05×10-6 E: 8.04×10-6 F: 1.07×10-5 G: 1.42×10-5 H: 1.89×10-5 1 2 1 2 1

Explanation / Answer

C1 = 6.55 F, C2 = 2.45 F, R1 = 22.5 , R2 = 23.5 , and 1 = 6.00 Volts.

R1 and R2 are in parallel

1/R = 1/R1 + 1/R2

1/R = 1/22.5 + 1/23.5

1/R = 0.044 + 0.042 = 0.086

R = 11.62 ohms

and C1 and C2 are in series

1/C = 1/C1 + 1/C2

1/C = 1/6.55 + 1/2.45

1/C = 0.15 + 0.408 = 0.558

C = 1.79 F

1)

the final amount of charge stored in C2

Q = C V

Q = 1.79 X 10-6 X 6

Q = 10.74 X 10-6 C

Q = 1.074 X 10-5 C

option : F

2)

Q = CV( 1 - exp(-t/RC))

Q = 2.45 X 10-6 X 6( 1 - exp(-5X10-6/11.62 X 2.45 X 10-6 ) )

Q = 2.45 X 10-6 X 6( 1 - 0.84 )

Q = 14.7 X 10-6 X 0.16

Q = 2.352 X 10-6 C

option : G

3)

i = V X exp(-t/RC)/ R

i = 6 X exp(-1) / 11.62

I = 6 X 0.36 / 11.62

i = 1.18×10-1 A

Option : C

4)

i = V X exp(-t/RC)/ R

i = 6 X exp(-5 X 10-6 / 11.62 X 1.79 X 10-6)/ 11.62

i = 6 X 0.78 / 11.62

i = 0.40

i = 4.0 X 10-1

option : B

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