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

Explanation

Given `Q = Q_0 [1-e^(alphat)]`
Here `Q_0 = Maximum charge and
`alpha = 1/(tau_c) = 1/(C_(Req))`
Now the maximum charge
`Q_0 = C[V_(0)]` where `V_0` = max potential difference across C
`= C[V/(R_1+R_2) xx R_2]`
and `tau_c = C R_(eq)`
`=C[(R_1R_2)/(R_1+R_2)] :. alpha = (1/tau_c) = (R_1 + R_2)/(CR_1R_2)`.