# 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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