Question

An air capacitor of capacitance $20\mu \text{F}$ is connected to a battery of $20\text{V}$. Now the space between its plates is completely filled with an insulator $(K=2)$. The magnitude of induced charge on the dielectric is

• A. $200\mu \text{C}$
• B. $100\mu \text{C}$
• C. $50\mu \text{C}$
• D. $400\mu \text{C}$

Answer 1

The correct option is A $200\mu \text{C}$

Initial charge on capacitor will be

$Q=CV=20\mu \text{F}\times 20\text{V}=400\mu \text{C}$

And we know that induced charge is given by the formula,

$Q_{in}=Q(1-\frac{1}{K})$

$\Rightarrow Q_{in}=400(1-\frac{1}{2})=200\mu \text{C}$

Hence, option $\left(A\right)$ is correct.