Question

Statement I: If the distance between parallel plates of a capacitor is halved and dielectric constant is made three times, then the capacitor becomes 6 times.
Statement II: Capacity of the capacitor does not depend upon the nature of the material.

• A. If both statements are true and statement II is the correct explanation of statement I.
• B. If both statements are true but statement II is not the correct explanation of statement I.
• C. If statement I is true but statement II is false.
• D. If both statements are false.

Answer 1

Answer: (B)

By the formula capacitance of a capacitor
$C_{1} =\varepsilon_{0} \times \frac{K A}{d} \propto \frac{K}{d}$
Hence, $\frac{C_{1}}{C_{2}} =\frac{K_{1}}{d_{1}} \times \frac{d_{2}}{K_{2}}$
$=\frac{K_{1}}{d_{1}} \times \frac{d_{1} / 2}{3 K}$
$=\frac{1}{6}$ or $C_{2}=6 C_{1}$
Again, for capacity of a capacitor, $C=\frac{Q}{V}$
Therefore, capacity of a capacitor -does not depend upon the nature of the material of the capacitor.