Question 112: Electrostats & Capacitance

Question

Identify the correct statements :A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.C. Increasing of area of capacitor plate or decreasing of 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 :

Accepted Answer

In a series combination, the effective capacitance ( $\mathrm{C}_{\mathrm{eff}}$ ) is given by :
$$ \frac{1}{\mathrm{C}_{\mathrm{eff}}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2}+\cdots+\frac{1}{\mathrm{C}_{\mathrm{n}}} $$
Mathematically, the sum of reciprocals always results in a total value that is less than any individual component. Hence, statement (A) is correct.
While dielectrics are insulators and do not allow the flow of current (conduction), they absolutely allow the displacement of charges. Under an external electric field, the molecules in a dielectric polarize, i.e., their positive and negative charges shift slightly in opposite directions. This is known as dielectric polarization.
Hence, the statement (B) is incorrect.
The capacitance $(C)$ of a parallel plate capacitor is given by:
$$ C=\frac{\kappa \epsilon_0 A}{d} $$
Where A is the area and d is the distance (thickness of dielectric).
If A increases, C increases $(\mathrm{C} \propto \mathrm{A})$.
If d decreases, C increases $\left(\mathrm{C} \propto \frac{1}{\mathrm{~d}}\right)$.
Hence, the statement (C) is correct.
The potential ( $V$ ) due to a point charge is $V=\frac{\mathrm{kq}}{\mathrm{r}}$. This means the potential depends only on the distance ( $r$ ) from the charge. For a fixed r , the potential is constant. All points at a constant distance r from a center form a spherical shell. Therefore, these concentric shells are equipotential surfaces.
Hence, the statement (D) is correct.
Statements A, C, and D are true, while statement B is false. Hence, the correct option is (A).

Answer

A, C and D Only

Answer

A, B and C Only

Answer

B and D Only

Answer

C and D Only

Electrostats & Capacitance

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