Question

Identify the correct statements:
[A.] Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the combination.
[B.] When a dielectric medium is placed between charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
[C.] Increasing area of a capacitor plate or decreasing thickness of dielectric is an alternate method to increase the capacitance.
[D.] For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below:

• A. C and D Only
• B. A, B and C Only
• C. B and D Only
• D. A, C and D Only

Hint:

In dielectrics, remember: no free charge flow, but polarization (bound charge displacement) always occurs.

Answer 1

The Correct Option is D

1. Understanding Statement A: The effective capacitance \(C_{\text{eq}}\) of capacitors in series is given by: \(\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}\) Since adding reciprocals always results in a smaller number, the effective capacitance in a series combination is always smaller than the smallest individual capacitor in the series. Hence, Statement A is correct.
2. Understanding Statement B: When a dielectric is introduced between charged plates of a capacitor, it does not conduct electricity due to its insulating properties. However, it can polarize, effectively leading to a re-distribution of internal charges without the movement of actual charge carriers (electrons) across the dielectric. This doesn’t prevent displacement current and hence doesn’t hinder the overall capacitance effect, which increases due to the dielectric. Thus, Statement B is incorrect.
3. Understanding Statement C: The capacitance \(C\) of a parallel plate capacitor is given by: \(C = \frac{\varepsilon A}{d}\), where \(A\) is the area of the plate and \(d\) is the thickness of the dielectric. Increasing the area \(A\) or decreasing the thickness \(d\) leads to an increase in capacitance. Thus, Statement C is correct.
4. Understanding Statement D: For a point charge, equipotential surfaces are indeed concentric spherical shells, with the charge at the center. This is part of the basic principles of electrostatics due to the radial nature of electric field lines emanating from or converging to a point charge. Therefore, Statement D is correct.

Conclusion: Based on the analysis, the correct statements are A, C, and D. The correct answer is: A, C and D Only.