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Question

A condenser in series with a resistor is connected through a switch to a battery of negligible internal resistance and having an emf of 12 V. One second after closing the switch, the condenser is found to have a potential difference of 6 V. The time constant of the system is:

A
2
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B
1ln2
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C
ln2
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D
ln(12)
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Solution

The correct option is B 1ln2
V0=12V
V=Io2=6V
6=12(1etRC)
etRC=12
etRC=2
t1RC=ln2
t=1Sec
1RC=ln2
Hence , τ=1ln2

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