A parallel-plate air capacitor is connected to a battery. While connected to the battery, a dielectric…
A parallel-plate air capacitor is connected to a battery. While connected to the battery, a dielectric medium whose dielectric constant is 2 is inserted, filling the space between the plates. The energy stored in the capacitor before the dielectric is inserted is \(E_{0}\). The energy stored is the capacitor after the dielectric has been inserted is \(E_{k}\). The ratio \(E_{k} / E_{0}\) is
Solution
Initial energy \(\frac{1}{2} \mathrm{CV}^{2}\)
After dielectric medium energy will be \(\frac{1}{2} C^{\prime} \bigvee^{2}\) and \(c^{\prime}=A \varepsilon / d \quad \varepsilon=\varepsilon E\)
\(\mathrm{u}^{\prime} / \mathrm{u}\) is as :
\(\begin{array}{l}
E_{R}=\frac{1}{2} C V^{2}=\frac{1}{2} \varepsilon_{r} C_{0} V^{2}=\varepsilon_{r} E_{0} \\
E_{R} / E_{0}=\varepsilon_{r}=2
\end{array}\)