An RC circuit is connected across a DC voltage source through an open switch. Th

Question

An RC circuit is connected across a DC voltage source through an open switch. The switch is closed at t = 0 s. Which of the following is a correct statement regarding this circuit?

The charge on the capacitor after one time constant is about 50% of its maximum value.
The charge on the capacitor after four time constants is about 98% of the maximum value.
The voltage on the capacitor after two time constants is about 14% of the maximum value.
The charge on the capacitor after one time constant is about 25% of its maximum value.
The voltage on this capacitor after two time constants is about 100% of its maximum value.

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Explanation / Answer

in RC circuit output voltage is given by
V o = V(final) + (V initial - V final)e^-t/

where = time constant

substitute = 4t we get 98% of maximum value

you can check by calculator by e^-t/ with =1t,2t,3t you get answer

so answer is

The charge on the capacitor after four time constants is about 98% of the maximum value.

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