Consider the RC circuit in the figure below. The switch was at position a for a

Question

Consider the RC circuit in the figure below. The switch was at position a for a long period of time and it is suddenly switched to position b at time t = 0.

For each statement select True or False.

-In the instant after the switch is thrown, the voltage across the capacitor is zero.

-In the instant after the switch is thrown the voltage across the resistor is zero.

-In the instant after the switch is thrown the current across the capacitor is zero.

-The current through the resistor equals the current across the capacitor at all times.

What is Vc at time t = 2.00 ms? Use the following data : R = 451.5 ?, C = 4.00 ?F, Vb = 2.15 V.

What is the total energy dissipated by the resistor R after the switch is thrown?

Explanation / Answer

False, the capacitor is already charged so there has to be come voltage across it.

False, there is a voltage across capacitor, so current in the circuit and hence voltage across resistor.

False,there is a voltage across capacitor, so current in the circuit and hence voltage across resistor.

True, as R and C are in series, so they will have same current all the time.

Given, R = 451.5 Ohm ; C = 4 x 10-6 F ; Vb = 2.15 V ; t = 2 ms = 2 x 10-3 s

We know that, Vc = Vb e-t/RC

Vc = 2.15 x e-2 x 10-3/451.5 x 4 x 10-6 = 2.15 x 0.33 = 0.7095 = 0.71 Volts(aprox)

Hence, Vc =  0.7095 = 0.71 Volts(aprox)

Energy dissipated would be equal to U = 1/2 C V2

U = 0.5 x 4 x 10-6 x 0.71 x 0.71 = 1 x 10-6 J

Hence, U = 1 x 10-6 J

Vc = 2.15 - 0.71 = 1.44 V

Hence, Vc' = 1.44 Volts.

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