A parallel plate capacitor of 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 the plate is `alpha`, find the coefficient of thernal expansion `(alphas)` of the spacers in order that the capacitance does not vary with temperature. (Ignore effect of the spacers on capacitance.)

Options

A. `alpha_(s) = (alpha)/(2)`
B. `alpha_(s) = 3alpha`
C. `alpha_(s) = 2alpha`
D. `alpha_(s) = alpha`

Answer

C

Explanation

`C=(in_(0)A)/(x)`, where x is separation between plates.
`(1)/(C )(dC)/(dT)=(1)/(A) (dA)/(dT)-(1)/(x)(dx)/(dT)`
For `(dC)/(dT) = 0, (1)/(x) (dx)/(dT)=(1)/(A) (dA)/(dT)`
`rArr alphas=2alpha`