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In the following table, the area of the plates and the separation between the plates are given for three capacitors. The figure shows their q–V graphs. Determine which graph is for which capacitor.
CapacitorAreaSeparation
C_1Ad
C_22Ad
C_3A2d

Asked in RS Academy GUJCET booklet · Capacitance of a conductor and a capacitor

Figure: Capacitance of a conductor and a capacitor
Answer: (3) 1 → C₂, 2 → C₁, 3 → C₃

Step-by-step solution

Given: C₁ has (A, d), C₂ has (2A, d), C₃ has (A, 2d).

Idea: C = (ε₀A)/d; write C₀ = (ε₀A)/d.

Then C₁ = C₀, C₂ = 2C₀ and C₃ = (C₀)/2.

On a q–V graph (q vertical, V horizontal) each capacitor is a straight line through the origin with slope q/V = C.

So the steepest line, 1, is the largest capacitance C₂; line 2 is C₁; the least steep line, 3, is C₃.

Answer: 1 → C₂, 2 → C₁, 3 → C₃.

Why the other options are wrong

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