In this RC circuit, R equals 120 ? and C equals 50.0 ?F. The battery voltage is

Question

In this RC circuit, R equals 120 ? and C equals 50.0 ?F. The battery voltage is 9.00 V. After closing the switch, what is the charge q on each plate after one time constant has passed?

Refer to the previous problem. After closing the switch, how much time passes before the charge reaches 360 ?C

In this RC circuit, R equals 120 ? and C equals 50.0 ?F. The battery voltage is 9.00 V. After closing the switch, what is the charge q on each plate after one time constant has passed? Refer to the previous problem. After closing the switch, how much time passes before the charge reaches 360 ?C

Explanation / Answer

Vc = V0 * 1 - e(-t / RC)

q / C = V0 * 1 - e(-t / RC)

q = C * V0 * 1 - e(-t / RC)

t / RC = 1

q = 50 * 10-6 * 9 * 1 - e(-1)

q = 2.85 * 10-4 C

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R * C = 120 * 50 x 10-6 = 0.006

360 * 10-6 = 50 x 10-6 * 9 * 1 - e(-t / RC)

360 x 10-6 = 50 x 10-6 * 9 * 1 - e(-t / 0.006)

360 * 10-6 = 50 * 10-6 * 9 * 1 - e(-t / 0.006)

e(-t / 0.006) = 0.20

-t / 0.006 = ln (0.20)

t = 0.00966 s

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