Two parallel-plate capacitors have the same plate area, and the gap between the plates is filled with a dielectric with a dielectric constant equal to 8. The gap in capacitor A is one half that in Capacitor B. What is the ratio of the capacitance of A to B? a). 4

b). 1/4

c). 1

d). 8

e). The ratio is not given

e). The ratio is not given

Explanation:

Capacitance of a capacitor

The expression for the capacitance of a capacitor with di electric material is given as

C=KεA/d

where

ε=permittivity of di electric

C= capacitance in farads

A= Area of plate

d= separating distance

K= dielectric constant

let the distance in capacitor B be 1mm

therefore the distance in A is 0.5mm

For the first (A) capacitor

C1=8εA/0.5

C1=16εA

For the Second (B) capacitor

C2=8εA/1

C2=8εA

the ratio of the capacitance of A to B

=C1/C2

=16εA/8εA

=2/1

=2

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