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Electrostatic Potential and Capacitance Set-4

Practice Important MCQs for Electrostatic Potential and Capacitance — Physics, Class 12.

This chapter is one of the most important parts of Class 12 Physics because it connects force, energy, and charge distribution in a very systematic way. Concepts like potential, potential energy, capacitance, dielectrics, and combinations of capacitors are repeatedly tested in CBSE boards as well as in JEE and NEET.

It is also a high-scoring chapter because many questions can be solved quickly once the core formulas and physical ideas are clear. A strong grasp of electrostatic potential and capacitance helps in numerical problems, conceptual MCQs, and practical applications involving energy storage and charge sharing.

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Q1. Two identical isolated capacitors of capacitance $C$ are initially such that one is charged to potential $V$ and the other is uncharged. They are then connected in parallel with like plates joined. The fraction of the initial electrostatic energy that is lost in the process is:

(A)

$\dfrac{1}{4}$

(B)

$\dfrac{1}{2}$

(C)

$\dfrac{3}{4}$

(D)

$\dfrac{1}{8}$

Q2. A parallel-plate capacitor has plate separation $d$ . A dielectric slab of dielectric constant $3$ and thickness $\dfrac{d}{3}$ fills the entire plate area, while the remaining thickness is vacuum. If a potential difference $V$ is maintained across the plates, the ratio of the potential drop across the dielectric slab to that across the vacuum region is:

(A)

$1:2$

(B)

$1:3$

(C)

$1:6$

(D)

$2:3$

Q3. Charges $+q$ and $-q$ are fixed at $x=+a$ and $x=-a$ respectively on the $x$ -axis. A point $P$ lies on the $y$ -axis at a distance $y$ from the origin. Which of the following statements is correct at $P$ ?

(A)

The potential is zero and the electric field is zero

(B)

The potential is non-zero and the electric field is zero

(C)

The potential is zero and the electric field is non-zero along the $x$ -axis

(D)

The potential is non-zero and the electric field is non-zero along the $y$ -axis

Q4. Two isolated conducting spheres of radii $R$ and $2R$ are initially at potentials $V$ and $2V$ respectively. They are connected by a thin wire and allowed to reach electrostatic equilibrium. The common potential after connection is:

(A)

$V$

(B)

$\dfrac{4V}{3}$

(C)

$\dfrac{5V}{3}$

(D)

$2V$

Q5. A capacitor of capacitance $C$ is connected to a battery of emf $V$ . Keeping the battery connected, a dielectric slab of dielectric constant $k$ is inserted so that the capacitor is completely filled. The ratio of the work done by the battery to the increase in stored electrostatic energy is:

(A)

$\dfrac{1}{2}$

(B)

$1$

(C)

$2$

(D)

$k$

Q6. A charge $+Q$ is placed at the center of a spherical conducting shell of radius $R$ that is initially neutral and isolated. If a small test charge is brought from infinity to a point just outside the shell, which of the following statements is most accurate about the work done by the electrostatic field in moving the test charge?

(A)

It is zero everywhere outside the shell because the conductor shields the field completely.

(B)

It is the same as if the shell and central charge together acted like a point charge $+Q$ at the center.

(C)

It depends on the path taken, because the induced charges make the field non-conservative.

(D)

It is zero only at the surface, but non-zero at all other external points.

Q7. Two identical parallel-plate capacitors, each of capacitance $C$ , are charged separately to the same potential difference $V$ and then disconnected from the battery. They are then connected in series with like plates joined together. Neglecting leakage, what is the final potential difference across each capacitor?

(A)

$\dfrac{V}{2}$

(B)

$V$

(C)

$\dfrac{3V}{2}$

(D)

$\dfrac{V}{4}$

Q8. A parallel-plate capacitor is connected to a battery and filled completely with a dielectric slab of relative permittivity $k$ . If the slab is slowly pulled out while the battery remains connected, which of the following quantities must decrease continuously during the process?

(A)

Charge on the capacitor plates remains constant

(B)

Electric field between the plates

(C)

Capacitance and stored energy

(D)

Potential difference across the plates

Q9. Three charges $+q$ , $+q$ , and $-q$ are placed at the vertices of an equilateral triangle of side $a$ . The electrostatic potential at the centroid is

(A)

$\dfrac{\sqrt{3}q}{4\pi\varepsilon_0 a}$

(B)

$0$

(C)

$\dfrac{2q}{4\pi\varepsilon_0 a}$

(D)

$\dfrac{q}{2\pi\varepsilon_0 a}$

Q10. A capacitor of capacitance $C$ is charged to potential $V_0$ , disconnected from the battery, and then a dielectric slab of dielectric constant $k$ is inserted completely between its plates. Which graph best represents the variation of electrostatic energy $U$ of the capacitor with $k$ ?

(A)

$U$ is independent of $k$

(B)

$U$ increases linearly with $k$

(C)

$U$ decreases as $\dfrac{1}{k}$

(D)

$U$ decreases as $\dfrac{1}{k^2}$

Q11. Two isolated conducting spheres of radii $R$ and $2R$ carry charges $+Q$ and $0$ , respectively. They are connected by a thin wire and allowed to reach electrostatic equilibrium. Which of the following is the final charge on the smaller sphere?

(A)

$Q/2$

(B)

$Q/3$

(C)

$2Q/3$

(D)

$3Q/4$

Q12. A charge $+q$ is moved slowly from the center of a uniformly charged non-conducting spherical shell of radius $R$ and total charge $Q$ to a point at distance $3R$ from its center. The change in electrostatic potential energy of the charge-shell system is:

(A)

$0$

(B)

$\dfrac{kQq}{3R}$

(C)

$-\dfrac{2kQq}{3R}$

(D)

$-\dfrac{kQq}{3R}$

Q13. A capacitor of capacitance $C$ is charged to a potential $V$ and then disconnected from the battery. A dielectric slab of dielectric constant $K$ completely fills the gap between the plates. Which quantity remains unchanged?

(A)

Capacitance

(B)

Potential difference

(C)

Energy stored

(D)

Charge on the capacitor

Q14. Two capacitors of capacitances $C$ and $2C$ are separately charged to potentials $V$ and $2V$ , respectively. They are then connected in parallel with like plates joined. The common final potential of the combination is:

(A)

$\dfrac{5V}{3}$

(B)

$\dfrac{3V}{5}$

(C)

$V$

(D)

$\dfrac{4V}{3}$

Q15. A parallel-plate capacitor of plate area $A$ and separation $d$ has its entire gap filled by two slabs placed one after the other along the field direction: one slab of thickness $d/2$ and dielectric constant $K$ , and the other slab of thickness $d/2$ with dielectric constant $1$ . The equivalent capacitance is:

(A)

$\dfrac{2K}{K+1}\,\dfrac{\varepsilon_0 A}{d}$

(B)

$\dfrac{K+1}{2K}\,\dfrac{\varepsilon_0 A}{d}$

(C)

$\dfrac{K}{K+1}\,\dfrac{\varepsilon_0 A}{d}$

(D)

$\dfrac{2(K+1)}{K}\,\dfrac{\varepsilon_0 A}{d}$

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