Assertion (A): If the distance between parallel plates of a capacitor is halved and dielectric constant is three times, then the capacitor becomes 6 times.
Reason (R): Capacity of a capacitor depends upon the nature of the plate material.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. For a parallel plate capacitor, \( C = \frac{\kappa \epsilon_0 A}{d} \). If ( d to d/2 ) and \( \kappa to 3\kappa \), then \( C' = \frac{3\kappa \epsilon_0 A}{d/2} = 6 \frac{\kappa \epsilon_0 A}{d} = 6C ). Reason (R) is false as capacitance depends on the dielectric medium, not the plate material.
Assertion (A): It is not possible to make a spherical conductor of capacitor one farad.
Reason (R): It is possible for earth as its radius is \( 6400 \text{ km} \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. For an isolated sphere, \( C = 4\pi \epsilon_0 R ). For \( C=1 \text{ F} \), \( R \approx 9 \times 10^9 \text{ m} \), which is astronomically large. Reason (R) is false. Earth's capacitance is \( C \approx 711 \mu\text{F} ), far less than 1 Farad.
Assertion (A): Electrolytic capacitors have larger capacities.
Reason (R): Electrolytic capacitors have a positive and a negative terminal.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true; electrolytic capacitors offer high capacitance due to their very thin dielectric layer and large effective plate area. Reason (R) is also true, as all capacitors have two terminals. However, the presence of terminals doesn't explain why they have *larger* capacities, so (R) is not the correct explanation for (A).
Assertion (A): In parallel plate capacitor separation ‘d’ should be smaller than the linear dimension of the plates \( d^2 << A\).
Reason (R): For \( d^2 << A \) a fringing effect can be ignored in the region sufficiently far from the edge.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true; for a parallel plate capacitor, 'd' must be much smaller than plate dimensions for the uniform field approximation. Reason (R) is also true. The condition \( d^2 << A \) (implying \( d << \sqrt{A} )\) allows ignoring fringing effects. Thus, (R) is the correct explanation for (A).