A parallel plate air capacitor has a capacitance `C`. When it is half filled with a dielectric `(K=2)`, the percentage increase in the cpacitance will be

Options

A. `25%`
B. `50%`
C. `75%`
D. `100%`

Answer

B

Explanation

`C_(1)=(K(A)/(2)in_(0))/(d)=2.(Ain_(0))/(2d)=(Ain_(0))/(d)=C`
`C_(2)=(A/(2)in_(0))/(d)=(Ain_(0))/(2d)=(c)/(2)`
`C_(1)` and `C_(2)` are in parallel (check polarity)
`C_(eq)=C_(1)+C_(2)=3C//2)`
Initial capacitance=`C`
Final capacitance=`(3C)/(2)`
`%` change: `((3C//2)/(c)-1)xx100=50%`