Four identical rectangular plates with length, l = 2 cm and breadth, b = 3/2 cm are arranged as shown in figure. The equivalent capacitance between A and C is (xε₀)/(d). The value of x is ______________. (Round off to the Nearest Integer) Numerical answer type. Work it out, then open the answer.

Answer: 2. Each facing pair forms C₀ = (ε₀ A)/(d) with A = lb = 2 × 3/2 = 3 cm². B and D are joined, so C faces B and D: the two capacitors C-B and C-D are in parallel, giving 2C₀. A-B ( C₀) is in series with this: CAC = (C₀ · 2C₀)/(3C₀) = 2/3C₀ = 2/3 · (3ε₀)/(d) = (2ε₀)/(d) (area in cm²) So x = 2.

Four identical rectangular plates with length, l = 2 cm and breadth… | JEE Main 2021 (17 Mar, Shift 1)

Q69JEE Main 2021 · 17 MAR · SHIFT 1Difficult

Combination of Capacitors

Four identical rectangular plates with length, l = 2 cm and breadth, b = $\frac{3}{2}$ cm are arranged as shown in figure. The equivalent capacitance between A and C is $\frac{x\varepsilon_0}{d}$ . The value of x is ______________. (Round off to the Nearest Integer)

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Each facing pair forms $C_0 = \frac{\varepsilon_0 A}{d}$ with $A = lb = 2 \times \frac{3}{2} = 3\ \text{cm}^2$ .
B and D are joined, so C faces B and D: the two capacitors C-B and C-D are in parallel, giving $2C_0$ .
A-B ( $C_0$ ) is in series with this: $C_{AC} = \frac{C_0 \cdot 2C_0}{3C_0} = \frac{2}{3}C_0 = \frac{2}{3} \cdot \frac{3\varepsilon_0}{d} = \frac{2\varepsilon_0}{d}$ (area in $\text{cm}^2$ )
So $x = 2$ .

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