The plates of a parallel plate capacitor are pulled apart with a velocity `v`. If at any instant their mutual distance of separation is `x`, then magnitude of rate of change of capacitance with respect to time varies as

Options

A. `(1)/(x)`
B. `(1)/(x^(2))`
C. `x^(2)`
D. `x`

Answer

B

Explanation

`C=(Ain_(0))/(x)=Ain_(0)x^(-1)`
`(dC)/(dt)=Ain_(0)(-1)x^(-2)(dx)/(dt)=-(Ain_(0))/(x^(2))v`
`|(dC)/(dt)|prop(1)/(x^(2))`