Q. $C,V,U$ and $Q$ are capacitance, potential difference, energy stored and charge of parallel plate capacitor respectively. The quantities that increases when a dielectric slab is introduced between the plates without disconnecting the battery are
A) $V$ and $C$
B) $V$ and $U$
C) $U$ and $Q$
D) $V$ and $Q$
Explanation
(c) Let $d$ be the distance between the plates and $k$ be the dielectric constant. Without disconnecting the battery, $V$ is the same
$E_{0} = \frac{\sigma}{\varepsilon_{0}};V_{0} = E_{0}d;C_{0} = \frac{Q}{V_{0}} = \frac{\varepsilon_{0}A}{d}$
With dielectric,
$V$ remains the same, capacitance increases, $U$ which is energy stored $\left( \frac{1}{2}CV^{2} \right)$ increases; $Q = CV,$ charge increases
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.