A circuit consisting of a capacitor $C$, a resistor of resistance $R$ and an ideal battery of emf $V$, as shown in figure is known as RC series circuit. As soon as the circuit is completed by closing key $S_1$ (keeping $S_2$ open) charges begin to flow between the capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference $V_c$ ($= q/C$) across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged ($Q = VC$). During this process of charging, the charge $q$ on the capacitor changes with time $t$ as $q = Q[1 - e^{-t/RC}]$ The charging current can be obtained by differentiating it and using $\frac{d}{dx}(e^{mx}) = me^{mx}$. Consider the case when $R = 20 \text{ k}\Omega$, $C = 500 \text{ }\mu\text{F}$ and $V = 10 \text{ V}$.

Year	Paper Code	Set	Position
CBSE 2025	Series 55-1	Set 1	Question 29
CBSE 2025	Series 55-1	Set 2	Question 30
CBSE 2025	Series 55-1	Set 3	Question 30

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)