2. Electric Potential and Capacitance
easy

A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K,$ which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect $?$

A

The energy stored in the capacitor decreases $K$ times.

B

The potential difference between the plates decreases $K$ times.

C

The change in energy stored is $\frac{1}{2}C{V^2}\left( {\frac{1}{K} - 1} \right)$ છે.

D

The charge on the capacitor is not conserved.

(AIPMT-2015)

Solution

$q=C V \Rightarrow V=q / C$

Due to dielectric insertion, new capacitance

$C_{2}=C K$

Initial energy stored in capacitor, $U_{1}=\frac{q^{2}}{2 C}$

Final energy stored in capacitor, $U_{2}=\frac{q^{2}}{2 K C}$

Change in energy stored, $\Delta U=U_{2}-U_{1}$

$\Delta U=\frac{q^{2}}{2 C}\left(\frac{1}{K}-1\right)=\frac{1}{2} C V^{2}\left(\frac{1}{K}-1\right)$

New potential difference between plates

$V^{\prime}=\frac{q}{C K}=\frac{V}{K}$

Standard 12
Physics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.