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Question

A resistor and a capacitor are connected as shown in the figure. The capacitor is originally given a charge of 5.0 μC and then discharged by closing the switch at t=0. At what time will the charge be equal to 0.50 μC. Given, C=1 μF, R=10 MΩ, ln(0.1)=2.3


A
23 s
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B
22 s
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C
21 s
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D
20 s
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Solution

The correct option is A 23 s
Given,

Initial charge, Q=5 μC,

Final charge, q=0.5 μC,

C=1 μF, R=10 MΩ,

For time t, we have t=RClnqQ t=10×106×1.0×106ln0.505.0

t=23 s

Hence, option (a) is the correct answer.

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