JEE Physics Electrostatic Potential and Capacitance MCQs Set 21

Physics Objective Questions and Answers: Electrostatic Potential and Capacitance

Explore reliable objective questions for Electrostatic Potential and Capacitance tailored for JEE learners. Utilizing these Physics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Download Electrostatic Potential and Capacitance MCQs with Answers

View or download the dedicated Electrostatic Potential and Capacitance MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Physics evaluations.

Multiple Choice Questions

Question 1: The capacitance of an isolated metallic sphere is 1 μF. Its radius is nearly
(a) 9 km
(b) 10 m
(c) 1.11 m
(d) 1.11 cm
Show Answer & Explanation

Answer: (a) 9 km

Explanation:
1. \( C=4\pi\varepsilon_0R\Rightarrow R=\dfrac{C}{4\pi\varepsilon_0}=9\times10^9\times10^{-6}=9\times10^3 \) m = 9 km.

Teacher's Note:
1. A farad is a very large unit.
2. Use \( 1/4\pi\varepsilon_0=9\times10^9 \).

Question 2: Two spherical conductors A and B of radii \( R \) and \( 2R \) are each given a charge \( Q \). When they are connected by a metallic wire, the charge will
(a) flow from A to B
(b) oscillate between A and B
(c) remain stationary
(d) flow from B to A
Show Answer & Explanation

Answer: (a) flow from A to B

Explanation:
1. Potentials: \( V_A=\dfrac{kQ}{R} \) and \( V_B=\dfrac{kQ}{2R} \).
2. A is at the higher potential, so positive charge flows from A to B until the potentials are equal.

Teacher's Note:
1. Charge moves from higher to lower potential.

Question 3: The capacitance of a parallel plate capacitor is \( C \). Its capacitance when the separation between the plates is halved will be
(a) C/2
(b) C/4
(c) \( 2C \)
(d) 4C
Show Answer & Explanation

Answer: (c) \( 2C \)

Explanation:
1. \( C=\varepsilon_0A/d\propto1/d \), so halving \( d \) doubles \( C \).

Teacher's Note:
1. Capacitance is inversely proportional to the separation.

Question 4: N identical mercury drops, each carrying the same charge, combine to form one big spherical drop. The capacitance of the bigger drop compared with that of each small drop is
(a) \( N^{5/3} \) times
(b) \( N^{2/3} \) times
(c) N times
(d) \( N^{1/3} \) times
Show Answer & Explanation

Answer: (d) \( N^{1/3} \) times

Explanation:
1. Volume conservation: \( R=N^{1/3}r \).
2. Capacitance of a sphere is proportional to its radius, so \( C'=N^{1/3}C \).

Teacher's Note:
1. Volume is conserved, not surface area.
2. C ∝ R for a sphere.

Question 5: If the potential difference across a 4 μF capacitor is 1.0 kilovolt, the electrical potential energy stored is
(a) 4 J
(b) 2 erg
(c) \( 4\times10^{-3} \) erg
(d) 2 J
Show Answer & Explanation

Answer: (d) 2 J

Explanation:
1. \( U=\tfrac12CV^2=\tfrac12\times4\times10^{-6}\times(10^3)^2=2 \) J.

Teacher's Note:
1. Use SI units: μF → 10⁻⁶ F, kV → 10³ V.

Question 6: A 2 μF capacitor is charged to 10 V. Another 4 μF capacitor is charged to 20 V. The two are connected in a single loop with the positive plate of one connected to the negative plate of the other. The heat evolved in the circuit is
(a) \( 600\ \mu\text J \)
(b) \( 900\ \mu\text J \)
(c) \( 300\ \mu\text J \)
(d) \( 450\ \mu\text J \)
Show Answer & Explanation

Answer: (a) \( 600\ \mu\text J \)

Explanation:
1. Charges 20 μC and 80 μC; opposite joining gives net 60 μC on 6 μF: \( V=10 \) V.
2. Initial energy \( \tfrac12\cdot2\cdot100+\tfrac12\cdot4\cdot400=900 \) μJ; final \( \tfrac12\cdot6\cdot100=300 \) μJ.
3. Heat \( =600 \) μJ.

Teacher's Note:
1. Heat = initial energy − final energy.

Question 7: A capacitor \( C_1=4 \) μF is connected in series with another capacitor \( C_2=1 \) μF across a 200 V dc source. The ratio of the potential across \( C_1 \) and \( C_2 \) is
(a) 2 : 1
(b) 1 : 2
(c) 4 : 1
(d) 1 : 4
Show Answer & Explanation

Answer: (d) 1 : 4

Explanation:
1. In series both carry the same charge, so \( V\propto1/C \).
2. \( V_1:V_2=C_2:C_1=1:4 \).

Teacher's Note:
1. Smaller capacitance takes the larger share of voltage.

Question 8: The parallel plates of a capacitor have an area of 0.2 m² and are \( 10^{-2} \) m apart. The original potential difference between them is 3000 V and it decreases to 1000 V when a sheet of dielectric is inserted so as to fill the whole space (battery disconnected). Take \( \varepsilon_0=9\times10^{-12} \) SI. The permittivity of the dielectric is
(a) \( 37\times10^{-12} \) C²N⁻¹m⁻²
(b) \( 28\times10^{-12} \) C²N⁻¹m⁻²
(c) \( 25\times10^{-12} \) C²N⁻¹m⁻²
(d) \( 27\times10^{-12} \) C²N⁻¹m⁻²
Show Answer & Explanation

Answer: (d) \( 27\times10^{-12} \) C²N⁻¹m⁻²

Explanation:
1. At constant charge \( V\propto1/K \): \( K=3000/1000=3 \).
2. Permittivity \( \varepsilon=K\varepsilon_0=27\times10^{-12} \) SI.

Teacher's Note:
1. Isolated capacitor: voltage falls by factor K.

Question 9: Two capacitors, each of capacitance \( C \), are connected in series with a battery of emf \( E \). A dielectric of constant \( K \) is inserted between the plates of one capacitor. The total charge flowing through the battery is
(a) \( \dfrac{KCE}{K+1} \)
(b) \( \dfrac{(K+1)CE}{2(K-1)} \)
(c) \( \dfrac{(K-1)CE}{2(K+1)} \)
(d) \( \dfrac{CE}{2K} \)
Show Answer & Explanation

Answer: (c) \( \dfrac{(K-1)CE}{2(K+1)} \)

Explanation:
1. Initial charge \( CE/2 \); final \( \dfrac{KCE}{K+1} \).
2. Difference \( =CE\dfrac{2K-(K+1)}{2(K+1)}=\dfrac{(K-1)CE}{2(K+1)} \).

Teacher's Note:
1. Same reasoning as for two identical capacitors in series.

Question 10: The distance between the plates of a charged, isolated parallel plate capacitor is 5 cm and the electric field inside is 200 V/cm. An uncharged metal bar of width 2 cm, with the same length as the plates, is fully immersed in the capacitor. The voltage across the capacitor after immersion is
(a) 100 V
(b) 600 V
(c) zero
(d) 400 V
Show Answer & Explanation

Answer: (b) 600 V

Explanation:
1. The charge is unchanged, so the field in the air gaps stays 200 V/cm.
2. The field inside the metal is zero, so the voltage is \( 200\times(5-2)=600 \) V.

Teacher's Note:
1. Isolated capacitor: charge, hence field, is fixed.

Question 11: The capacity and the energy stored in a parallel plate condenser with air between its plates are \( C_0 \) and \( W_0 \) respectively. If the air is replaced by glass (\( K=5 \)) at constant charge, the capacity and the energy stored will be
(a) \( C_0/5 \), \( W_0/5 \)
(b) \( 5C_0 \), \( W_0/5 \)
(c) \( 5C_0 \), \( 5W_0 \)
(d) \( C_0/5 \), \( 5W_0 \)
Show Answer & Explanation

Answer: (b) \( 5C_0 \), \( W_0/5 \)

Explanation:
1. Capacitance becomes \( KC_0=5C_0 \).
2. At constant charge \( U=Q^2/2C \) falls to \( W_0/5 \).

Teacher's Note:
1. Constant charge: energy ∝ 1/C.

Question 12: A glass slab is put between the plates of a charged, isolated parallel plate condenser. Which of the following quantities does NOT change?
(a) the intensity of the electric field
(b) the charge
(c) the capacity
(d) the energy of the condenser
Show Answer & Explanation

Answer: (b) the charge

Explanation:
1. The condenser is isolated, so the charge remains constant.
2. The capacity rises by \( K \), the field and the energy fall by \( K \).

Teacher's Note:
1. Isolated: Q constant.

Question 13: Two capacitors of 8 μF and 16 μF have breaking voltages of 20 V and 80 V respectively. They are combined in series. The maximum charge they can store individually in the combination is
(a) \( 200\ \mu C \)
(b) \( 1280\ \mu C \)
(c) \( 160\ \mu C \)
(d) \( 320\ \mu C \)
Show Answer & Explanation

Answer: (c) \( 160\ \mu C \)

Explanation:
1. Charge limits: \( 8\times20=160 \) μC and \( 16\times80=1280 \) μC.
2. In series the same charge flows on both, so the smaller limit, 160 μC, applies.

Teacher's Note:
1. Use the smaller charge limit.

Question 14: Three capacitors of 2 μF, 4 μF and 6 μF are connected in parallel to a 10 V battery. The work done by the battery in charging them is
(a) \( 1300\ \mu J \)
(b) \( 1600\ \mu J \)
(c) \( 1500\ \mu J \)
(d) \( 1200\ \mu J \)
Show Answer & Explanation

Answer: (d) \( 1200\ \mu J \)

Explanation:
1. Total charge \( 120 \) μC drawn at 10 V: \( W=QV=120\times10=1200 \) μJ.
2. Half of this (600 μJ) is stored and half is dissipated.

Teacher's Note:
1. Battery work is QV, twice the stored energy.

Question 15: Two dielectric slabs of constants \( K_1 \) and \( K_2 \), each of thickness \( d/2 \), fill the space between the plates (area \( A \), separation \( d \)) of a capacitor, one above the other (parallel to the plates). The capacitance is
(a) \( \dfrac{2\varepsilon_0A}{d}\,\dfrac{K_1+K_2}{K_1K_2} \)
(b) \( \dfrac{2\varepsilon_0A}{d}\,\dfrac{K_1K_2}{K_1+K_2} \)
(c) \( \dfrac{d}{2\varepsilon_0A} \)
(d) \( \dfrac{2\varepsilon_0A}{d}(K_1+K_2) \)
Show Answer & Explanation

Answer: (b) \( \dfrac{2\varepsilon_0A}{d}\,\dfrac{K_1K_2}{K_1+K_2} \)

Explanation:
1. Two layers in series: \( C_1=\dfrac{2K_1\varepsilon_0A}{d} \) and \( C_2=\dfrac{2K_2\varepsilon_0A}{d} \).
2. Series: \( C=\dfrac{C_1C_2}{C_1+C_2}=\dfrac{2\varepsilon_0A}{d}\dfrac{K_1K_2}{K_1+K_2} \).

Teacher's Note:
1. Layers parallel to the plates are in series.

Question 16: The capacitance of a parallel plate capacitor is 2.5 μF. When it is half filled with a dielectric (the dielectric occupying half the plate area, side by side), its capacitance becomes 5 μF. The dielectric constant of the dielectric is
(a) 0.33
(b) 3
(c) 7.5
(d) 4
Show Answer & Explanation

Answer: (b) 3

Explanation:
1. Parallel combination: \( C=\dfrac{C_0}{2}+\dfrac{KC_0}{2}=\dfrac{C_0}{2}(1+K) \).
2. So \( 5=1.25(1+K) \) and \( K=3 \).

Teacher's Note:
1. Side-by-side regions are in parallel.

Question 17: A capacitor stores 60 μC of charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 120 μC flows through the battery. The dielectric constant of the material inserted is
(a) 1
(b) 2
(c) 4
(d) 3
Show Answer & Explanation

Answer: (d) 3

Explanation:
1. Final charge \( =60+120=180 \) μC at the same voltage.
2. Charge is proportional to capacitance: \( K=180/60=3 \).

Teacher's Note:
1. The battery keeps the potential fixed.

Question 18: A capacitor stores 60 μC of charge when connected across a battery (initial capacitance 2 μF). When the gap between the plates is filled with a dielectric, a charge of 120 μC flows through the battery. The heat produced in the process is
(a) \( 900\ \mu J \)
(b) \( 1800\ \mu J \)
(c) \( 2700\ \mu J \)
(d) \( 3600\ \mu J \)
Show Answer & Explanation

Answer: (b) \( 1800\ \mu J \)

Explanation:
1. Battery voltage \( V=60/2=30 \) V; battery work \( =120\times30=3600 \) μJ.
2. Stored energy rises from \( \tfrac12\times60\times30=900 \) μJ to \( \tfrac12\times180\times30=2700 \) μJ, an increase of 1800 μJ.
3. Heat \( =3600-1800=1800 \) μJ.

Teacher's Note:
1. Heat = work by battery − increase in stored energy.

Question 19: A parallel plate condenser is immersed in oil of dielectric constant 2 (isolated, charged). The field between the plates is
(a) decreased to one-half
(b) decreased to \( 1/\sqrt2 \)
(c) increased by a factor \( \sqrt2 \)
(d) increased to twice
Show Answer & Explanation

Answer: (a) decreased to one-half

Explanation:
1. With the same free charge, \( E=\dfrac{E_0}{K}=\dfrac{E_0}{2} \).

Teacher's Note:
1. Dielectrics weaken the field by the factor K.

Question 20: A capacitor of capacitance 100 μF is connected across a battery of emf 6.0 V through a resistance of 20 kΩ for 4.0 s. The battery is then replaced by a thick wire. The charge on the capacitor 4.0 s after the battery is disconnected is
(a) 60 μC
(b) 70 μC
(c) 30 μC
(d) 80 μC
Show Answer & Explanation

Answer: (b) 70 μC

Explanation:
1. \( \tau=RC=2 \) s. Charge after 4 s of charging: \( q=600(1-e^{-2})=519 \) μC.
2. Discharging for another 4 s: \( q=519\,e^{-2}\approx70 \) μC.

Teacher's Note:
1. First find the charge at the end of charging.

Question 21: A parallel plate capacitor is made by stacking \( n \) equally spaced plates connected alternately. If the capacitance between any two adjacent plates is \( C \), the resultant capacitance is
(a) (n + 1)C
(b) C
(c) \( (n-1)C \)
(d) nC
Show Answer & Explanation

Answer: (c) \( (n-1)C \)

Explanation:
1. \( n \) plates form \( (n-1) \) gaps, each of capacitance \( C \), all connected in parallel.
2. Total \( (n-1)C \).

Teacher's Note:
1. Count the gaps, not the plates.

Question 22: A fully charged capacitor of capacitance \( C \) is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat \( s \) and mass \( m \). If the temperature of the block rises by \( \Delta T \), the potential difference \( V \) across the capacitor was
(a) \( \dfrac{mC\Delta T}{s} \)
(b) \( \sqrt{\dfrac{2mC\Delta T}{s}} \)
(c) \( \dfrac{ms\Delta T}{C} \)
(d) \( \sqrt{\dfrac{2ms\Delta T}{C}} \)
Show Answer & Explanation

Answer: (d) \( \sqrt{\dfrac{2ms\Delta T}{C}} \)

Explanation:
1. All the stored energy becomes heat: \( \tfrac12CV^2=ms\Delta T \).
2. So \( V=\sqrt{\dfrac{2ms\Delta T}{C}} \).

Teacher's Note:
1. Energy conservation.

Question 23: A parallel plate capacitor has two circular plates separated by 5 mm with a dielectric of constant 2.2 between them. When the electric field in the dielectric is \( 3\times10^4 \) V/m, the charge density of the positive plate will be close to
(a) \( 6\times10^{4} \) C/m²
(b) \( 6\times10^{-7} \) C/m²
(c) \( 3\times10^{4} \) C/m²
(d) \( 3\times10^{-7} \) C/m²
Show Answer & Explanation

Answer: (b) \( 6\times10^{-7} \) C/m²

Explanation:
1. Free charge density \( \sigma=K\varepsilon_0E=2.2\times8.85\times10^{-12}\times3\times10^4 \).
2. This equals \( 5.8\times10^{-7}\approx6\times10^{-7} \) C/m².

Teacher's Note:
1. In a dielectric \( E=\sigma/K\varepsilon_0 \).

Question 24: The two plates of a capacitor have equal and opposite charges \( Q \). The dielectric between them has dielectric constant \( K \) and resistivity \( \rho \). The leakage current carried by the dielectric is
(a) \( \dfrac{Q\rho}{K\varepsilon_0} \)
(b) \( \dfrac{QK}{\varepsilon_0\rho} \)
(c) \( \dfrac{Q}{K\varepsilon_0\rho^2} \)
(d) \( \dfrac{Q}{K\varepsilon_0\rho} \)
Show Answer & Explanation

Answer: (d) \( \dfrac{Q}{K\varepsilon_0\rho} \)

Explanation:
1. Resistance of the dielectric \( R=\rho\dfrac dA \); capacitance \( C=\dfrac{K\varepsilon_0A}{d} \).
2. Voltage \( V=Q/C \), current \( i=\dfrac VR=\dfrac{Q}{RC}=\dfrac{Q}{K\varepsilon_0\rho} \).

Teacher's Note:
1. RC = Kε₀ρ is independent of geometry.

Free study material for Physics

Practice MCQs for JEE Physics Electrostatic Potential and Capacitance

About Electrostatic Potential and Capacitance MCQs for JEE Physics

Explore reliable practice questions for Electrostatic Potential and Capacitance tailored for JEE Physics learners. Use these multiple-choice formats to evaluate preparedness and strengthen problem-solving skills.

How to Verify Your MCQ Answers

Cross-reference your completed choices with comprehensive NCERT solutions for JEE Physics to ensure absolute clarity across all sub-topics in this chapter.

Enhance Speed with Online MCQ Tests

Explore our broader library of printable assignments, chapter notes, and mock tests designed to support continuous revision and secure higher marks in JEE assessments.

FAQs

Where can I access latest JEE Physics Electrostatic Potential and Capacitance MCQs Set 21?

You can get most exhaustive JEE Physics Electrostatic Potential and Capacitance MCQs Set 21 for free on StudiesToday.com. These MCQs for JEE Physics are updated for the 2026-27 academic session as per JEE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Physics JEE material?

Yes, our JEE Physics Electrostatic Potential and Capacitance MCQs Set 21 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the JEE paper is now competency-based.

How do practicing Physics MCQs help in scoring full marks in JEE exams?

By solving our JEE Physics Electrostatic Potential and Capacitance MCQs Set 21, JEE students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Physics.

Do you provide answers and explanations for JEE Physics Electrostatic Potential and Capacitance MCQs Set 21?

Yes, Physics MCQs for JEE have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused JEE exams.

Can I practice these Physics JEE MCQs online?

Yes, you can also access online interactive tests for JEE Physics Electrostatic Potential and Capacitance MCQs Set 21 on StudiesToday.com as they provide instant answers and score to help you track your progress in Physics.