A capacitor is connected to a 20   V battery through a resistance of 10 Ω . It is found that the…

A capacitor is connected to a 20 V battery through a resistance of 10Ω. It is found that the potential difference across the capacitor rises to 2 V in 1 μs. The capacitance of the capacitor is ________μF.
Given In 109=0.105
  1. 0.95
  2. 9.52
  3. 1.85
  4. 0.105

Solution

V=V01-e-t/RC

2=201-e-1μs10C

110=1-e-1×10-610C

e-1×10-610C=910

1×10-610C=ln109

C=1×10-610×ln109=10-71.05=11.05μF=100105μF=0.95μF

Asked in: JEE Main 2021 (01 Sep Shift 2)

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