Question

In an RC circuit, the total resistance is 15000 ohms and the battery’s emf is 24.0 V. If the time constant is measured to be 35 x 10 - 6 sec calculate (a) the total capacitance of

the circuit and (b) the time it takes for the voltage across the resistor, Vr to reach 16.0 V after the switch is closed.

Answer 1

Part A.

In RC circuit time constant is given by:

tau = RC

C = tau/R

Using given values:

tau = 35*10^-6 sec

R = 15000 ohm

C = 35*10^-6/15000 = 2.33*10^-9 F

C = 2.33 nF

Part B.

In a discharging RC circuit Voltage is given by:

V = V0*(exp (-t/tau))

exp (-t/tau) = V/V0

t = -tau*ln (V/V0)

Using known values:

t = -35*10^-6*ln (16/24)

t = 14.2*10^-6 sec = 14.2 s

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