Question

A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ____.

Answer 1

Correct answer is : 2

Without dielectric

\(Q = \frac {A\in_0}{d}V\)

with dielectric

\(Q =\frac {A \in _0 \,V}{d-t + \frac {t}{K}}\)

given

\(\frac {A \in _ 0 V}{d-t + \frac {t}{K}} = (1.25)\frac {A\,\in_0 V}{d}\)

\(\Rightarrow 1.25 \left(3+\frac {2}{K}\right)=5\)

\(\Rightarrow K=2\)

Answer 2

the answer to this question is as below