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

Statement-wise analysis: A. Effective capacitance of a series combination is always smaller than the smallest capacitance. For capacitors in series: \[ \frac{1}{C_{\text{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+\cdots \] Hence, \[ C_{\text{eq}}<\min(C_1,C_2,\dots) \] True. B. No displacement of charges occurs inside a dielectric. This statement is false. In a dielectric, bound charges do get displaced slightly due to polarization, even though free charge flow does not occur. C. Increasing area or decreasing separation increases capacitance. Capacitance of a parallel plate capacitor: \[ C=\frac{\varepsilon A}{d} \] Thus, increasing plate area \(A\) or decreasing separation \(d\) increases \(C\). True. D. Equipotential surfaces for a point charge are concentric spheres. Electric potential due to a point charge depends only on distance \(r\): \[ V=\frac{kq}{r} \] Hence, all points at the same distance form spherical equipotential surfaces. True.
Step 2: Collect correct statements Correct statements are: \[ \boxed{A,\ C,\ D} \] Final Answer: \[ \boxed{\text{(D) A, C and D Only}} \]