Question

A paralle plate capacitor of capacitance $90$ pF is connected to a battery of emf $20$V. If a dielectric material of dielectric constant K$=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be.

• A. $2.4$ n C
• B. $0.9$ n C
• C. $1.2$ n C
• D. $0.3$ n C

Answer 1

Answer: (C)

$1.2$ n C

For parallel plate capacitor

$Q=CV$

Initial charge $Q_i=90pf\times 20V=1.8nC$

When dielectric material is inserted

$C=KC$

Final charge $Q_f=\left(KC\right)V=\frac{5}{3}\times 90pF\times 20v$=$3nC$

Induced charge =$Q{}_f-Q_i$

$=3-1.8=1.2nC$