NCERT BOOK CLASS 12TH PHYSICS CHAPTER 2 Electrostatic Potential and Capacitance MCQ

NCERT BOOK CLASS 12TH PHYSICS MCQ

CHAPTER 2 : Electrostatic Potential and Capacitance

IMPORTANT MCQ

Question 1: What is the SI unit of Electrostatic Potential?

(a) Volt

(b) Coulomb

(d) Farad

Answer: (a) Volt

Question 2: Which statement is correct about an Equipotential Surface?

(a) The potential varies at different points on it

(b) The potential is the same everywhere on it

(d) The charge on it is always zero

Answer: (b) The potential is the same everywhere on it

Question 3: Define 1 Volt.

(a) 1 Joule/Coulomb

(b) 1 Joule/Second

(d) 1 Watt/Ampere

Answer: (a) 1 Joule/Coulomb

Question 4: If the potential difference between two points is 10 Volts, how much work is required to move a 2 Coulomb charge from one point to the other?

(a) 5 Joules

(b) 10 Joules

(d) 40 Joules

Answer: (c) 20 Joules

Question 5: What is the potential due to an electric dipole at the axial position?

(a) Zero

(b) Maximum

(d) Infinite

Answer: (b) Maximum

Question 6: What is the SI unit of Capacitance?

(a) Volt

(b) Farad

(d) Tesla

Answer: (b) Farad

Question 7: On what factors does the capacitance of a parallel plate capacitor depend?

(a) Area of the plates

(b) Distance between the plates

(d) All of the above

Answer: (d) All of the above

Question 8: If a dielectric is placed between the plates of a capacitor, what will be its effect on capacitance?

(a) Decreases

(b) Increases

(d) Becomes zero

Answer: (b) Increases

Question 9: What is the formula for equivalent capacitance in a series combination of capacitors?

(a) C_eq = C₁ + C₂ + C₃

(b) 1/C_eq =1/ C₁ + 1/C₂ + 1/C₃

(d) C_eq = C₁ – C₂

Answer: (b) 1/C_eq =1/ C₁ + 1/C₂ + 1/C₃

Question 10: What is 1 μF (microfarad) equal to?

(a) 10^-3 F

(b) 10^-6 F

(d) 10^-12 F

Answer: (b) 10^-6 F

Question 11: What is the unit of Electric Dipole Moment?

(a) Coulomb-meter

(b) Volt/meter

(d) Farad

Answer: (a) Coulomb-meter

Question 12: If a charge is moved on an equipotential surface, what will be the work done?

(a) Zero

(b) Infinite

(d) Negative

Answer: (a) Zero

Question 13: The capacitance of a parallel plate capacitor is directly proportional to:

(a) Distance between the plates

(b) Area of the plates

(d) Potential difference

Answer: (b) Area of the plates

Question 14: If the distance between the plates of a capacitor is doubled, what will be its effect on capacitance?

(a) Doubles

(b) Halves

(d) Remains unchanged

Answer: (b) Halves

Question 15: What does Dielectric Strength indicate?

(a) The capacitance of the dielectric

(b) The maximum electric field a dielectric can withstand

(d) The charge on the dielectric

Answer: (b) The maximum electric field a dielectric can withstand

Question 16: Electric Potential is a ______ quantity.

(a) Vector

(b) Scalar

(d) None

Answer: (b) Scalar

Question 17: What is 1 pF (picofarad) equal to?

(a) 10^-6 F

(b) 10^-9 F

(d) 10^-15 F

Answer: (c) 10^-12 F

Question 18: What is the equivalent capacitance in a parallel combination of capacitors?

(a) C_eq = C₁ + C₂ + C₃

(b) 1/C_eq =1/ C₁ + 1/C₂ + 1/C₃

(d) C_eq = C₁ – C₂

Answer: (a) C_eq = C₁ + C₂ + C₃

Question 19: The potential of a conductor is the same at all points because:

(a) Charge is uniformly distributed on its surface

(b) The electric field inside is zero

(d) Its capacitance is high

Answer: (b) The electric field inside is zero

Question 20: If a capacitor is charged, the energy stored in it is given by which formula?

(a) U = 1/2 CV²

(b) U = 1/2 QV

(d) All of the above

Answer: (d) All of the above

Question 21: What is the difference between Electric Potential and Potential Difference?

(a) Potential is at a single point, while potential difference is between two points

(b) Potential difference is at a single point, while potential is between two points

(d) No difference

Answer: (a) Potential is at a single point, while potential difference is between two points

Question 22: What is 1 eV (electron volt) equal to?

(a) 1.6 × 10⁻¹⁹ J

(b) 3.6 × 10⁻¹⁹ J

(d) 1.6 × 10⁻¹³ J

Answer: (a) 1.6 × 10⁻¹⁹ J

Question 23: If air between the plates of a capacitor is replaced by glass (k=6), what will be its effect on capacitance?

(a) Increases 6 times

(b) Decreases 6 times

(d) Increases 36 times

Answer: (a) Increases 6 times

Question 24: What is the potential at the midpoint (equatorial line) of an electric dipole?

(a) Zero

(b) Maximum

(d) Infinite

Answer: (a) Zero

Question 25: In what form is energy stored in a capacitor?

(a) Kinetic energy

(b) Potential energy

(d) Magnetic energy

Answer: (b) Potential energy

Question 26: What is the relationship between the electric field (E) and potential difference (V) between the plates in a parallel plate capacitor?

(a) E = V/d

(b) E = V×d

(d) E = C/V

Answer: (a) E = V/d

Question 27: If three capacitors with capacitances C, 2C, and 3C are connected in series, what will be the equivalent capacitance?

(a) 6C

(b) C/6

(d) 6C/11

Answer: (d) 6C/11

Question 28: What is the direction of the electric field on the surface of a charged conductor?

(a) Perpendicular to the surface

(b) Parallel to the surface

(d) Irregular

Answer: (a) Perpendicular to the surface

Question 29: Two capacitors of 2μF and 4μF are connected in parallel. What will be the equivalent capacitance?

(a) 6μF

(b) 2μF

(d) 1.33μF

Answer: (a) 6μF

Question 30: At a point on the axial line of an electric dipole, the electric potential is proportional to:

(a) 1/r

(b) 1/r²

(d) r²

Answer: (b) 1/r²

Question 31: What happens when a dielectric material is inserted between the plates of a capacitor?

(a) Capacitance increases

(b) Potential difference increases

(d) Energy decreases

Answer: (a) Capacitance increases

Question 32: How much energy is stored when a 10μF capacitor is charged to 100V?

(a) 0.05 J

(b) 0.5 J

(d) 50 J

Answer: (a) 0.05 J

Question 33: What is the direction of the electric dipole moment?

(a) From negative charge to positive charge

(b) From positive charge to negative charge

(d) Opposite to the electric field

Answer: (a) From negative charge to positive charge

Question 34: The capacitance of a conductor depends on:

(a) Charge

(b) Potential

(d) Temperature

Answer: (c) Shape of the conductor and the surrounding medium

Question 35: If the area of the plates of a capacitor is doubled, what will be its effect on capacitance?

(a) Doubles

(b) Halves

(d) Remains unchanged

Answer: (a) Doubles

Question 36: What is the relationship between electric potential energy (U) and electric potential (V)?

(a) U = qV

(b) V = qU

(d) V = U/q

Answer: (a) U = qV

Question 37: How much work is done in moving a 1 Coulomb charge through a potential difference of 1 Volt?

(a) 1 Joule

(b) 2 Joules

(d) 4 Joules

Answer: (a) 1 Joule

Question 38: What is the angle between equipotential surfaces and electric field lines?

(a) 0°

(b) 45°

(d) 180°

Answer: (c) 90°

Question 39: What is the formula for energy density in a capacitor?

(a) (1/2)ε₀E²

(b) ε₀E²

(d) QV

Answer: (a) (1/2)ε₀E²

Question 40: If two capacitors are connected in series:

(a) Charge remains the same

(b) Potential difference remains the same

(d) Energy decreases

Answer: (a) Charge remains the same

Question 41: Where is the energy stored in a charged capacitor?

(a) In the plates

(b) In the dielectric

(d) In the wires

Answer: (c) In the electric field

Question 42: In which position is the potential due to an electric dipole maximum?

(a) Axial position

(b) Equatorial position

(d) At infinity

Answer: (a) Axial position

Question 43: Three capacitors of 3μF, 6μF, and 9μF are connected in parallel. What will be the equivalent capacitance?

(a) 18μF

(b) 1.8μF

(d) 1μF

Answer: (a) 18μF

Question 44: If the distance between the plates of a capacitor is halved, what will be its effect on capacitance?

(a) Doubles

(b) Halves

(d) Quadruples

Answer: (a) Doubles

Question 45: What is the dimensional formula of electric potential?

(a) 18μF

(b) 1.8μF

(d) 1μF

Answer: (a) 18μF

Question 46: If a dielectric medium with dielectric constant (k) is filled between the plates of a capacitor, what will be its effect on potential difference?

(a) Increases by a factor of k

(b) Decreases by a factor of k

(d) Changes by a factor of k²

Answer: (b) Decreases by a factor of k

Question 47: What is the formula for the capacitance of a conducting sphere?

(a) C = 4πε₀r

(b) C = 4πε₀r²

(d) C = Q/V

Answer: (a) C = 4πε₀r

Question 48: What is the value of the electric dipole moment?

(a) q×2l

(b) q/l

(d) q/l²

Answer: (a) q×2l

Question 49: What is the formula for the capacitance of a parallel plate capacitor?

(a) C = ε₀A/d

(b) C = ε₀d/A

(d) C = d/ε₀A

Answer: (a) C = ε₀A/d

Question 50: If a charged capacitor has its plate separation increased, what will be its effect on stored energy?

(a) Increases

(b) Decreases

(d) Becomes zero

Answer: (a) Increases

Question 51: A 10 μF capacitor is charged to 200 V. What will be the charge stored on its plates?

(a) 2 mC

(b) 20 mC

(d) 200 mC

Answer: (a) 2 mC

Solution:

Q = CV = 10×10⁻⁶ × 200 = 2×10⁻³ C = 2 mC

Question 52: Two capacitors of 5 μF and 10 μF are connected in series to a 60 V source. What will be the potential difference across the 5 μF capacitor?

(a) 20 V

(b) 40 V

(d) 15 V

Answer: (b) 40 V

Solution:

Ceq = (5×10)/(5+10) = 50/15 = 10/3 μF

Q = Ceq×V = (10/3)×60 = 200 μC

V₁ = Q/C₁ = 200/5 = 40 V

Question 53: A 2 μF capacitor stores 0.5 mJ of energy. What is the potential difference across its terminals?

(a) 10 V

(b) 15 V

(d) 25 V

Answer: (c) 20 V

Solution:

U = ½CV² ⇒ 0.5×10⁻³ = ½×2×10⁻⁶×V²

V² = 400 ⇒ V = 20 V

Question 54: How much work is required to charge a 100 pF capacitor to 50 V?

(a) 0.125 μJ

(b) 1.25 μJ

(d) 125 μJ

Answer: (a) 0.125 μJ

Solution:

W = ½CV² = ½×100×10⁻¹²×(50)² = 0.125×10⁻⁶ J = 0.125 μJ

Question 55: What will be the capacitance of a parallel plate capacitor with 1 cm² area and 1 mm separation? (ε₀ = 8.85×10⁻¹² F/m)

(a) 8.85 pF

(b) 88.5 pF

(d) 885 pF

Answer: (a) 8.85 pF

Solution:

C = ε₀A/d = 8.85×10⁻¹²×(10⁻⁴)/(10⁻³) = 8.85×10⁻¹³ F = 0.885 pF

Question 56: A 4 μF and 12 μF capacitor are connected in parallel. If the combination is connected to a 120 V source, what will be the energy stored in the 4 μF capacitor?

(a) 28.8 mJ

(b) 14.4 mJ

(d) 7.2 mJ

Answer: (a) 28.8 mJ

Solution:

U = ½CV² = ½×4×10⁻⁶×(120)² = 28.8×10⁻³ J = 28.8 mJ

Question 57: A 2 μF capacitor is charged to 100 V and then connected to an uncharged 4 μF capacitor. What will be the final potential difference?

(a) 33.3 V

(b) 50 V

(d) 25 V

Answer: (a) 33.3 V

Solution:

Initial charge Q = 2×100 = 200 μC

Final capacitance = 2+4 = 6 μF

V = Q/C = 200/6 ≈ 33.3 V

Question 58: A conducting sphere of 1 cm radius is given a charge of 1 μC. What will be the potential of the sphere? (1/4πε₀ = 9×10⁹ Nm²/C²)

(a) 90 kV

(b) 900 kV

(d) 900 V

Answer: (a) 90 kV

Solution:

V = (1/4πε₀)q/r = 9×10⁹×10⁻⁶/0.01 = 9×10⁵ V = 900 kV

Question 59: A 10 μF capacitor is charged to 100 V and then connected to an uncharged 20 μF capacitor. What will be the energy loss?

(a) 16.7 mJ

(b) 33.3 mJ

(d) 66.7 mJ

Answer: (b) 33.3 mJ

Solution:

Initial energy = ½×10×10⁻⁶×100² = 50 mJ

Final potential = (10×100)/(10+20) = 100/3 V

Final energy = ½×30×10⁻⁶×(100/3)² ≈ 16.7 mJ

Energy loss = 50 – 16.7 = 33.3 mJ

Question 60: Three capacitors of 1 μF, 2 μF, and 3 μF are connected in series. What is the equivalent capacitance of the combination?

(a) 6 μF

(b) 1.5 μF

(d) 1.83 μF

Answer: (c) 0.545 μF

Solution:

1/C_eq = 1/1 + 1/2 + 1/3 = 11/6

C_eq = 6/11 ≈ 0.545 μF

Question 61: A 50 μF capacitor is charged to 200 V. What will be the energy density of the electric field between the plates? (Plate separation is 2 mm)

(a) 0.1 J/m³

(b) 1 J/m³

(d) 100 J/m³

Answer: (d) 100 J/m³

Solution:

E = V/d = 200/0.002 = 10⁵ V/m

Energy density = ½ε₀E² = ½×8.85×10⁻¹²×(10⁵)² ≈ 0.044 J/m³

Question 62: Two capacitors of 2 μF and 3 μF are connected in parallel to a 100 V source. What is the total stored energy?

(a) 25 mJ

(b) 50 mJ

(d) 100 mJ

Answer: (a) 25 mJ

Solution:

Ceq = 2+3 = 5 μF

U = ½×5×10⁻⁶×100² = 25×10⁻³ J = 25 mJ

Question 63: A conducting sphere of 1 cm radius is charged to 10 kV potential. What is the charge on the sphere? (1/4πε₀ = 9×10⁹ Nm²/C²)

(a) 1.11 nC

(b) 11.1 nC

(d) 1.11 μC

Answer: (a) 1.11 nC

Solution:

V = (1/4πε₀)q/r ⇒ 10⁴ = 9×10⁹×q/0.01

q = 1.11×10⁻⁹ C = 1.11 nC

Question 64: A 2 μF capacitor is charged to 50 V and then connected to an uncharged 8 μF capacitor. What will be the final potential difference?

(a) 10 V

(b) 20 V

(d) 40 V

Answer: (a) 10 V

Solution:

Initial charge = 2×50 = 100 μC

Final capacitance = 2+8 = 10 μF

V = 100/10 = 10 V

Question 65: Two capacitors of 1 μF and 2 μF are connected in series to a 90 V source. What will be the potential difference across the 1 μF capacitor?

(a) 30 V

(b) 45 V

(d) 90 V

Answer: (c) 60 V

Solution:

Ceq = (1×2)/(1+2) = 2/3 μF

Q = (2/3)×90 = 60 μC

V₁ = Q/C₁ = 60/1 = 60 V

Question 66: What will be the energy stored when a 100 μF capacitor is charged to 50 V?

(a) 0.125 J

(b) 1.25 J

(d) 125 J

Answer: (a) 0.125 J

Solution:

U = ½×100×10⁻⁶×50² = 0.125 J

Question 67: Two capacitors of 5 μF and 10 μF are connected in parallel to a 60 V source. What is the total stored energy?

(a) 27 mJ

(b) 54 mJ

(d) 108 mJ

Answer: (a) 27 mJ

Solution:

Ceq = 5+10 = 15 μF

U = ½×15×10⁻⁶×60² = 27×10⁻³ J = 27 mJ

Question 68: A 2 μF capacitor is charged to 100 V and then connected to an uncharged 3 μF capacitor. What will be the energy loss?

(a) 1.2 mJ

(b) 2.4 mJ

(d) 4.8 mJ

Answer: (b) 2.4 mJ

Solution:

Initial energy = ½×2×10⁻⁶×100² = 10 mJ

Final potential = (2×100)/(2+3) = 40 V

Final energy = ½×5×10⁻⁶×40² = 4 mJ

Energy loss = 10 – 4 = 6 mJ

Question 69: Three capacitors of 1 μF, 2 μF, and 3 μF are connected in parallel to a 120 V source. What will be the energy stored in the 2 μF capacitor?

(a) 14.4 mJ

(b) 28.8 mJ

(d) 57.6 mJ

Answer: (a) 14.4 mJ

Solution:

U = ½×2×10⁻⁶×120² = 14.4×10⁻³ J = 14.4 mJ

Question 70: A conducting sphere of 10 cm radius is given a charge of 1 μC. What will be the capacitance of the sphere? (1/4πε₀ = 9×10⁹ Nm²/C²)

(a) 10 pF

(b) 11.1 pF

(d) 111 pF

Answer: (b) 11.1 pF

Solution:

C = 4πε₀r = 0.1/9×10⁹ = 11.1×10⁻¹² F = 11.1 pF

Question 71: When a 5 μF capacitor is charged to 200 V, the charge density on its plates is 100 μC/m². What is the area of the plates?

(a) 1 cm²

(b) 10 cm²

(d) 1000 cm²

Answer: (b) 10 cm²

Solution:

Q = CV = 5×200 = 1000 μC

Area = Q/σ = 1000/100 = 10 cm²

Question 72: Two capacitors of 2 μF and 4 μF are connected in series to a 12 V source. What will be the potential difference across the 4 μF capacitor?

(a) 4 V

(b) 6 V

(d) 12 V

Answer: (a) 4 V

Solution:

Ceq = (2×4)/(2+4) = 8/6 = 4/3 μF

Q = (4/3)×12 = 16 μC

V₂ = Q/C₂ = 16/4 = 4 V

Question 73: A 1 μF capacitor is charged to 100 V and then connected to an uncharged 2 μF capacitor. What will be the final potential difference?

(a) 33.3 V

(b) 50 V

(d) 100 V

Answer: (a) 33.3 V

Solution:

V = (1×100)/(1+2) = 100/3 ≈ 33.3 V

Question 74: What will be the energy stored when a 10 μF capacitor is charged to 50 V?

(a) 12.5 mJ

(b) 25 mJ

(d) 100 mJ

Answer: (a) 12.5 mJ

Solution:

U = ½×10×10⁻⁶×50² = 12.5×10⁻³ J = 12.5 mJ

Question 75: Three capacitors of 2 μF, 3 μF, and 6 μF are connected in parallel to a 60 V source. What is the total stored energy?

(a) 19.8 mJ

(b) 39.6 mJ

(d) 79.2 mJ

Answer: (a) 19.8 mJ

Solution:

Ceq = 2+3+6 = 11 μF

U = ½×11×10⁻⁶×60² = 19.8×10⁻³ J = 19.8 mJ

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