1.

In the previous question, calculate the time required for the potential difference across capacitor to become equal to that across resistor.

Answer»

13.86s
4.86s
9.2s
21.63s

Solution :Charge as a function of time can be written as: `q= q_(0) (1-E^(-t//tau)) rArr q= CV_(0) (1- e^(-t//RC))` On differentiating charge we can write current as a function of time:
`i= (dq)/(dt) = CV_(0) (0 + (1)/(RC) e^(-t//RC)) = (V_(0))/(R ) e^(-t//RC)`
POTENTIAL difference across capacitor = Potential difference across resistor
`rArr q//C = iR`
`rArr V_(0) (1-e^(-t//RC)) = V_(0) e^(-t//RC)`
`rArr e^(-t//RC) = (1)/(2) rArr e^(t//RC) = 2`
`rArr (t)/(RC) = ln 2 rArr t = RC (ln 2)`
`=(5 xx 10^(6)) (4 xx 10^(-6)) (0.693) = 13.86s` HENCE, option (a) is correct


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