In the circuit below, C = 4.67 ?F, and R = 4481.0 ?. The capacitor carries a cha

Question

In the circuit below, C = 4.67 ?F, and R = 4481.0 ?. The capacitor carries a charge q0 = 7.49 ?C when the switch S is closed at t = 0 s.

Find:

(a) The time constant of the circuit.

? =___ ms.

(b) The charge on the capacitor at t = 0.02 s.

qC (0.02 s) =____ ?C.

(d) The percentage of the total charge on the capacitor at t = ?.

qC%(?) = ____% of q0.

(e) The actual value of the charge on the capacitor at t = ?.

qC (?) =____ ?C

In the circuit below, C = 4.67 ?F, and R = 4481.0 ?. The capacitor carries a charge q0 = 7.49 ?C when the switch S is closed at t = 0 s. Find: (a) The time constant of the circuit. ? =___ ms. (b) The charge on the capacitor at t = 0.02 s. qC (0.02 s) =____ ?C. (d) The percentage of the total charge on the capacitor at t = ?. qC%(?) = ____% of q0. (e) The actual value of the charge on the capacitor at t = ?. qC (?) =____ ?C

Explanation / Answer

a) T = R*C

= 4481*4.67*10^-6

= 0.02093 s or 20.93 ms

b) q = Qo*e^(-t/T)

= 7.49*10^-6*e^(-0.02/0.02093)

= 2.88 micro C

d) at t = T

q = Qo*e^(-t/T)

= Qo/e

= 37% of Qo

d) q = 0.37*7.49*10^-6

= 2.77 micro C

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