Assertion (A): Capacitor reduces sparks in induction coil.
Reason (R): Capacitor provides alternative path to current when circuit is broken.
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
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A: True. In an induction coil, breaking the circuit induces a high back EMF, causing sparks across the switch. Capacitors are used to mitigate this.
R: True. A capacitor connected across the switch provides a path for the induced current, absorbing the inductive energy and preventing excessive voltage buildup that leads to sparks.\n(R) correctly explains how (A) works.
Assertion (A): If temperature is increased, the dielectric constant of a polar dielectric decreases whereas that of a non-polar dielectric does not change significantly.
Reason (R): The magnitude of dipole moment of individual polar molecule decreases significantly with increase in temperature.
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
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A: True. Increased temperature reduces the alignment of polar molecules, decreasing their dielectric constant. Non-polar dielectrics are less affected.
R: False. The magnitude of an *individual* dipole moment is largely temperature independent. It is the *average alignment* of these dipoles that decreases due to thermal agitation. Therefore, (A) is true and (R) is false.
Assertion (A): A capacitor of a certain capacity, whenever charged, will always store the same amount of charge.
Reason (R): A definite capacity implies always a same definite value of charge.
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
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A: False. The charge stored by a capacitor is \(Q = CV\). For a given capacitance \(C\), the charge \(Q\) depends on the applied voltage \(V\), which can vary.\nR: False. A definite capacity \(C\) does not imply a definite charge \(Q\), as \(Q\) is also proportional to the voltage \(V\) across the capacitor, which can be varied.\nTherefore, both (A) and (R) are false.
A capacitor of capacitance C is connected across a battery of potential difference V.
Assertion (A): The energy stored in capacitor is \( \frac{1}{2} CV^2 \).
Reason (R): The energy supplied by the battery is \( CV^2 \).
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
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Assertion (A) is true: energy stored in a capacitor is \( U = \frac{1}{2} CV^2 \). Reason (R) is true: the total work done by the battery (energy supplied) is \( W = CV^2 \). However, (R) is not the correct explanation for (A), as half of the supplied energy is dissipated as heat.
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
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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
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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
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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
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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).
Assertion (A): Two protons placed at different distances, between the plates of a parallel plate capacitor experience the same force.
Reason (R): The electric field between the plates of parallel plate capacitor is constant.
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
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Assertion (A) is true because the electric field (E) in a parallel plate capacitor is uniform. The force on a proton (q) is F = qE , which is constant. Reason (R) is true as the electric field between plates of an ideal parallel plate capacitor is constant. (R) correctly explains (A).