A capacitor initially given a charge `Q_(0)` is connected across a resistor `R` at `t=0`. The separation between the plates changes according to `d=(d_(0))/((1+t))(0 le t lt1)`. A small bulb is connected across the plates of the capacitor which lights when potential difference across the plates of the capacitor reaches `V_(0)`. Find
(`a`) the variation of charge with time
(`b`) time when the bulb will light.

Explanation

To solve the problem step by step, we will analyze the behavior of the capacitor and the resistor, and derive the required expressions for charge variation and the time when the bulb lights up.

### Step 1: Understand the relationship between charge, capacitance, and voltage.
The charge \( Q \) on a capacitor is related to the capacitance \( C \) and the voltage \( V \) across it by the equation:
\[ Q = C \cdot V \]

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