1.

At time t=0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them beocme 4V? `[Take : In 5 = 1.6, In3 = 1.1]`. .

Answer» Here, supply voltage, `V_(s) = 10 vol t`.
Effective resistance,
`R = (2xx2)/(2+2) = 1 M Omega = 10^(6) Omega`
Effective capacitanace,
`C = 2+2 = 4 muF = 4xx10^(-6)F`
While charging the capacitor with voltage applied, voltage across the capacitor is given by
`V_(c) = V_(s) [1-e^(-t//RC )]=10 [1-e^(-t//10^(6))xx4xx10^(-6)]`
`4 = 10 [1-e^(-t//4)]`
`1-e^(-t//4) = (4)/(10) = 0.4`
`e^(-t//4) = 1 - 0.4 = 0.6`
`- (t)/(4) log_(e) e = log_(e) 0.6 = log_(e) ((3)/(5)) = log_(e) 3 - log_(e) 5`
`- (t)/(4) = 1.1 - 1.6 = -0.5`
`t = 4xx0.5 = 2s`


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