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A parallel plate capacitor of area A and...

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.)

A

`alpha_(s) = (alpha)/(2)`

B

`alpha_(s) = 3alpha`

C

`alpha_(s) = 2alpha`

D

`alpha_(s) = alpha`

Text Solution

Verified by Experts

The correct Answer is:
C
`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`
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