Question 179: Electrostatics & Capacitance

Question

A parallel plate air capacitor has a capacitance $C$. When it is half filled as shown in figure with a dielectric constant $K = 5$, the percentage increase in the capacitance is ________.

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

33.34

Answer

66.67

Answer

200

Answer

400

Electrostatics & Capacitance

A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant K = 5, the percentage increase in the capacitance is ________.

Choose the correct answer: