In the given circuit, the switch S is closed at time t = 0 . The charge Q on the capacitor at any instant t is given by `Q(t) = Q(1-e^(-alphat))`. Find the value of `Q_0` and `alpha` in terms of given parameters as shown in the circuit.
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Answer

A, B, C, D

Explanation

For loop (1)
`V- (l_(1)+l_(2))R-(q)/(C ) = 0 ..(1)`
Fro loop (2)
`(q)/(C )-l_(1)R_(2) = 0 ….(2)` ltbgt and `l_(1) =(dq)/(dt) …(3)`
From (1),(2) and (3)
`overset(q)underset(0) Ò(dq)/(CR_(2)V-q(R_(1)+R_(2)))= Ò(dt)/(R,C)`
`q=(CR_(2)V)/(R_(1)+R_(2)) overset(æ)underset(e)(ç)1-e^(-(R_(1)+R_(2))/(R_(1)C)t)underset(ø)underset(-:)underset(-:)(ddoto)`
`Q = CV_(eq) (1-e^(-t//R_(eq)C)) = (CR_(2)V)/(R_(1)+R_(2)) [1-e^(-((R_(1)+R_(2)t))/(R_(1)R_(2)C))]`
`Q_(0) = (CR_(2)V)/(R_(1)+R_(2)), alpha = (R_(1)+R_(2))/(R_(1)R_(2)C)`