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Consider a series RC circuit at the left where C- 6 F, R-2 and -20 V. You close

ID: 779273 • Letter: C

Question

Consider a series RC circuit at the left where C- 6 F, R-2 and -20 V. You close the switch at t -0. Find (a) the time constant for theE circuit, (b) the half-life of the circuit, (c) the current at t 0, (d) the voltage across the capacitor att 0, and (e) the voltage across the resistor after a very long time. Given the circuit at the right in which the following values are used: R1 5 RI R2 V. You close the switch at t 0. Find (a) the current through R2 at t-0, and (b) the voltage across R1 after a long time.

Explanation / Answer

1)

a) Time constant of the ckt, T = R*C

= 2*10^6*6*10^-6

= 12 s

b) I = Imax*e^(-t/T)

0.5*Imax = Imax*e^(-t1/2/T)

ln(0.5) = -(t1/2)/T

==> t1/2 = -T*ln(0.5)

= -12*ln(0.5)

= 8.32 s

c) at t = 0, I = 0

d) at t = 0, V_C = V_battery

= 20 V

e) after a long time, V_R = 0

because, the poetetial drops at resistor.