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.

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.

Tardigrade Admin · Accepted Answer

By the formula capacitance of a capacitor

C_{1} = ε_{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.

Q. 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.

If both statements are true and statement II is the correct explanation of statement I.

If both statements are true but statement II is not the correct explanation of statement I.

If statement I is true but statement II is false.

If both statements are false.

Q. 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.