A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges $Q$ and $-Q$ with potential difference $V = V_1 - V_2$ between them. The ratio $\frac{Q}{V}$ is a constant, denoted by $C$ and is called the capacitance of the capacitor. It is independent of $Q$ or $V$. It depends only on the geometrical configuration (shape, size, separation) of the two conductors and the medium separating the conductors. When a parallel plate capacitor is charged, the electric field $E_0$ is localised between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (charge density $\sigma$), the dielectric is polarised by the field. Consequently opposite charges appear on the faces of the slab, near the plates, with surface charge density of magnitude $\sigma_p$. For a linear dielectric $\sigma_p$ is proportional to $E_0$. Introduction of a dielectric changes the electric field, and hence, the capacitance of a capacitor, and hence, the energy stored in the capacitor. Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel. (i) Consider a capacitor of capacitance $C$, with plate area $A$ and plate separation $d$, filled with air [Fig. (a)]. The distance between the plates is increased to $2d$ and one of the plates is shifted as shown in Fig. (b). The capacitance of the new system now is :

Year	Paper Code	Set	Position
CBSE 2025	Series 55-6	Set 1	Question 29
CBSE 2025	Series 55-6	Set 2	Question 30
CBSE 2025	Series 55-6	Set 3	Question 29

• 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)