Question

A capacitor when filled with a dielectric $K = 3$ has charge $Q_{0}$, voltage$V_{0}$ and field $E_{0}$. If the dielectric is replaced with another one having K = 9, the new values of charge, voltage and field will be respectively

• A. $3Q_{0},3V_{0},3E_{0}$
• B. $Q_{0},3V_{0},3E_{0}$
• C. $Q_{0},\frac{V_{0}}{3},3E_{0}$
• D. $Q_{0},\frac{V_{0}}{3},\frac{E_{0}}{3}$

Answer 1

Answer: (D)

$Q_{0},\frac{V_{0}}{3},\frac{E_{0}}{3}$

Answer 2

Suppose, charge, potential difference and electric field for capacitor without dielectric medium are Q, V and E respectively

With dielectric medium of $K = 3$

With dielectric medium of $K = 9$

Charge $Q_{0} = Q$ Charge $Q' = Q = Q_{0}$

Potential difference $V_{0} = \frac{V}{3}$

Potential difference $V' = \frac{V}{9} = \frac{V_{0}}{3}$

Electric field $E_{0} = \frac{E}{3}$

Electric field $E' = \frac{E}{9} = \frac{E_{0}}{3}.$