Question

A parallel plate capacitor of plate area A and separation d is provided with thin insulating spacers to keep its plates aligned in an environment of fluctuating temperature. If the coefficient of thermal expansion of material of plate is a then the coefficient of thermal expansion (a_S) of the spacers in order that the capacitance does not vary with temperature (ignore effect of spacers on capacitance)

• A. $\alpha_{S} = \frac{\alpha}{2}$
• B. a_S = 3a
• C. a_S = 2a
• D. a_S = a

Answer 1

Answer: (C)

a_S = 2a

Answer 2

C = $\frac{\varepsilon_{0}A}{x}$, where x is separation between plates

$\frac{1}{C}\frac{dC}{dT}$= $\frac{1}{A}\frac{dA}{dT}$ – $\frac{1}{x}\frac{dx}{dT}$

for $\frac{dC}{dT}$= 0, $\frac{1}{x}\frac{dx}{dT}$= $\frac{1}{A}\frac{dA}{dT}$Ž a_S = 2a