1) Immediately after the battery is disconnected, what is the voltage across the

Question

1)  Immediately after the battery is disconnected, what is the voltage across the capacitor? How do you know?

2)  After the battery has been disconnected for a long time, what is the voltage across the resistor? How do you know?

3) The time constant for an RC circuit is the amount of time it takes the capacitor to gain 63.2% of its charge (charging) or lose 63.2% of its charge (discharging). It is also equal to the time it takes the current to fall by 63.2% in an RC circuit. Using this information, find the value for C, the capacitance of the capacitor? How do you know?

Explanation / Answer

1) It will have maximum voltage since it will be fully charged.

2) zero, capacitor would have lost its energy to resistor in the form of heat.

3) The time constant for an RC circuit is equal to the time it takes the current to fall by 63.2% in an RC circuit.

From the graph we see that maximum current in the circuit = 20 A which is the condition at t = 0 s

This circuit is discharging , so when 63.2 percent has discharged, remaining current = 100-63.2 percent = 36.7 percent

So, 63.2 percent of 20 A = 0.632*20 = 12.64 A

So, remaining current = 20-12.64 = 7.36 A

From the graph, we see that when current = 7.36 A, time = 5 s

So, the time constant = 5 s <----by definition of time constant as explained above

But time constant of the circuit = R*C

So, C = time constant/R = 5/R

Just put the value of R to get the answer

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