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← JEE Main 2022 · 30 Jul · Shift 2
PhysicsInteger+4 / -1Question 25 of 90

JEE Main 2022 · 30 Jul · Shift 2, Physics question 25

Combination of four parallel plate air capacitors is shown in figure. Separation between the plate P1_1 & P2_2 is d3\dfrac d3 and separation between the plates P2_2 and P3_3 is d. The equivalent capacitance of the configuration is _______ μF.

(Given ϵ0Ad=4\dfrac{\epsilon_0A}d=4 μF. Where A = Area of plates)

Plates P1, P2, P3 stacked: P1 and P2 are d/3 apart and divided into three sections of areas A/6, A/3 and A/2; P2 and P3 are d apart.
Answer and worked solution

Official answer: 3

Upper gap (d/3): three sections in parallel, 3×4(16+13+12)=123\times4\left(\frac16+\frac13+\frac12\right)=12 μF. Lower gap (d, full area): 4 μF.

In series 12×416=3\frac{12\times4}{16}=3 μF.

Answer: 3