Question

In the following table, the area of plates and separation between the plates are given. In the nearby Figure, q - V graphs for them are shown. Determine which graph is for which capacitor.
(Capacitor - area - separation)
C1 - A - d
C2 - 2A - d
C3 - A - 2d
(A) 1 → C2 2 → C3 3 → C1
(B) 1 → C1 2 → C2 3 → C3(C) 1 → C2 2 → C1 3 → C3(D) 1 → C3 2 → C1 3 → C2

Answer 1

we know the relation between capacitor , area and separation.
e.g., $\mathbb{C}=\frac{\epsilon_0A}{d}$
hence, capacitor is directly proportional to area and inversely proportional to separation.

Given, C1 - A - d
so, $C_1=\frac{\epsilon_0A}{d}$....(i)

C2 - 2A - d
so, $C_2=\frac{2\epsilon_0A}{d}$....(ii)

C3 - A - 2d
so, $C_3=\frac{\epsilon_0A}{2d}$....(iii)

also we know, q = CV
at constant value of V , higher the capacitance of capacitor , higher will be charge.
e.g., higher the slope of Q/V graph , higher will be capacitance of capacitor.

from equations (i), (ii) and (iii)
C2 > C1 > C3

hence, graph -1 => C2
graph - 2 => 1
graph - 3 => 3

hence, option (C) is correct.