Electrostatic Potential and Capacitance — Class 12 MCQs with Answers

Electrostatic Potential and Capacitance — important questions & MCQs with answers (Class 12 Physics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   SI unit of electric potential:

   AWattBNewtonCVoltDTesla
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   Answer: Volt

   Explanation: Potential is defined as work done per unit charge, V = W/q, so its SI unit is joule per coulomb — the volt. Watt and tesla measure power and magnetic field, not potential.

2. Q2 of 6Easy

   SI unit of capacitance:

   AVoltBFaradCOhmDCoulomb
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   Answer: Farad

   Explanation: Capacitance C = Q/V, charge per unit potential, so its SI unit is coulomb per volt — the farad. Ohm measures resistance and volt measures potential, not charge storage.

3. Q3 of 6Medium

   Potential energy of charge q at potential V:

   AqVBq/VCq²VDV/q
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   Answer: qV

   Explanation: Since potential V is work done per unit charge, the potential energy of a charge q sitting at that point is simply U = qV — not q/V, which would have the wrong units.

4. Q4 of 6Medium

   Assertion (A): A capacitor with air between plates 1 cm apart can be charged only to a potential difference of about 3 × 10⁴ V before the air breaks down. Reason (R): The dielectric strength of a medium is the smallest electric field at which the medium becomes polarised.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: A is true but R is false

   Explanation: A is true: the dielectric strength of air is about 3 × 10⁶ V m⁻¹, and V = Ed = 3 × 10⁶ V m⁻¹ × 0.01 m = 3 × 10⁴ V. R is false: dielectric strength is the maximum electric field a dielectric can withstand without breakdown of its insulating property; any field polarises a dielectric.

5. Q5 of 6Hard

   Three charges +q at vertices of equilateral triangle of side a. Total PE of system:

   

   A3kq²/aBkq²/aC6kq²/aDkq²/(3a)
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   Answer: 3kq²/a

   Explanation: Total potential energy sums every unique pair: three pairs each separated by a, all contributing kq²/a, giving 3kq²/a — not 6kq²/a, which would double-count each pair.

6. Q6 of 6Hard

   Assertion (A): A 2 μF capacitor and a 4 μF capacitor joined in series across a 12 V battery have potential differences of 4 V and 8 V across them respectively. Reason (R): In a series combination, the potential difference across each capacitor is inversely proportional to its capacitance.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: A is false but R is true

   Explanation: In series both capacitors carry the same charge, so V = Q/C and the smaller capacitor takes the larger share. C = (2 × 4)/(2 + 4) = 4/3 μF and Q = 16 μC, giving 8 V across the 2 μF and 4 V across the 4 μF capacitor, so A has them reversed and is false. R is true.

Electrostatic Potential and Capacitance notes: key concepts (Class 12 Physics)

Energy in electrostatics: potential and potential energy, how the field is the negative gradient of potential, equipotential surfaces, conductors and electrostatic shielding, dielectrics and polarisation, capacitance and the parallel plate capacitor, series and parallel combinations, and the energy stored in a charged capacitor.

Electrostatic potential energy

The work done by an external agent in assembling a configuration of charges from infinite separation, brought together without acceleration.

Electric potential

The potential energy per unit charge at a point, measured in volts. It is a SCALAR, which makes it far easier to work with than the field.

Potential of a point charge

Varies as q/r and, unlike the field, carries the sign of the charge — so the potential near a negative charge is genuinely negative.

Relation between E and V

The field is the negative gradient of potential, E = −dV/dr. Field points from high to low potential, in the direction of steepest fall.

Equipotential surfaces

Surfaces of constant potential, always perpendicular to the field lines. No work is done moving a charge anywhere along one.

Potential due to a dipole

Falls off as 1/r² and is ZERO everywhere on the equatorial plane, where the contributions of the two charges cancel exactly.

Potential energy of a system

The sum of the pairwise potential energies of every distinct pair of charges in the configuration.

PE of a dipole in a field

Equal to −p·E, so it is minimum when the dipole aligns with the field (stable) and maximum when anti-parallel (unstable).

Conductors in electrostatics

Field inside is zero, the whole conductor is at one potential, excess charge sits on the surface, and the surface field is perpendicular to it.

Electrostatic shielding

A cavity inside a conductor has zero field regardless of external charges — the principle behind the Faraday cage and why a car is safe in lightning.

Dielectrics and polarisation

An insulator placed in a field develops an induced dipole moment that opposes the applied field, reducing the net field inside by a factor K.

Capacitance

The charge stored per unit potential difference, measured in farads. It is fixed by geometry and the dielectric alone, never by the charge stored.

Parallel plate capacitor

Its capacitance rises with plate area and falls with separation. Inserting a dielectric of constant K multiplies the capacitance by K.

Capacitors in series and parallel

Series capacitors share the same CHARGE and their reciprocals add; parallel capacitors share the same VOLTAGE and simply add. This is opposite to resistors.

Energy stored in a capacitor

Equal to ½CV², the work done in charging it. Half the energy supplied by a battery is always lost as heat during charging.

Energy density of the field

The stored energy can be regarded as residing in the field itself, at ½ε₀E² per unit volume — a picture essential for electromagnetic waves.