A capacitor when filled with a dielectric \(\mathrm{K}=3\) has charge \(\mathrm{Q}_{0}\), voltage…

A capacitor when filled with a dielectric \(\mathrm{K}=3\) has charge \(\mathrm{Q}_{0}\), voltage \(\mathrm{V}_{0}\) and field \(\mathrm{E}_{0}\). If the dielectric is replaced with another one having \(\mathrm{K}=9\) after disconnecting it with the battery the new values of charge, voltage and field will be respectively
  1. \(3 \mathrm{Q}_{0}, 3 \mathrm{~V}_{0}, 3 \mathrm{E}_{0}\)
  2. \(\mathrm{Q}_{0}, 3 \mathrm{~V}_{0}, 3 \mathrm{E}_{0}\)
  3. \(Q_{0}, \frac{V_{0}}{3}, 3 E_{0}\)
  4. \(Q_{0}, \frac{V_{0}}{3}, \frac{E_{0}}{3}\)

Solution

When there is no battery, charge remains same while potential difference and electric field decreases
i.e. \(Q^{\prime}=Q_{0}, V^{\prime}=\frac{V_{0} \times 3}{9}=\frac{V_{0}}{3}\) and
\(E^{\prime}=\frac{E_{0} \times 3}{9}=\frac{E_{0}}{3}\) ~

Asked in: JEE Mains - Capacitance - Chapter Test

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