Infinite RC Circuit!

In the circuit shown, we have infinitely many resistors with resistance of \( R_1 = R, R_2 = \frac{R}{2}, R_3 = \frac{R}{4} , \ldots\). We also have infinitely many capacitors with capacitance of \( C_1 = C, C_2 = 2C, C_3 = 4C ,\ldots \). At \(t=0\) switch S is closed.

Find the ratio of potential drop (in volts) across capacitor \( C_n\) and resistor \(R_n\) at time \(t=R_\text{eq}C_\text{eq}\). Take \(e=2.718\).

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