Electrostatics - Electrostatic Potential & Capacitance
Q. A capacitor is charged to a potential difference of V. If the charge on the capacitor is Q, what is the capacitance? (2023)
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A.
Q/V
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B.
V/Q
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C.
QV
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D.
V^2/Q
Solution
The capacitance C is defined as C = Q/V.
Correct Answer: A — Q/V
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Q. A capacitor of capacitance C is charged to a voltage V. What is the charge stored in the capacitor? (2023)
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A.
C/V
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B.
CV
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C.
V/C
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D.
C^2V
Solution
The charge Q stored in a capacitor is given by Q = CV.
Correct Answer: B — CV
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Q. If the capacitance of a parallel plate capacitor is C, what will be the capacitance if the distance between the plates is doubled? (2020)
Solution
The capacitance C of a parallel plate capacitor is given by C = εA/d. If the distance d is doubled, the new capacitance will be C/2.
Correct Answer: A — C/2
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Q. If the distance between the plates of a capacitor is halved, what happens to the capacitance? (2019)
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A.
It doubles
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B.
It halves
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C.
It remains the same
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D.
It quadruples
Solution
If the distance d is halved, the capacitance C = εA/d will double.
Correct Answer: A — It doubles
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Q. The potential energy stored in a capacitor is given by which of the following formulas? (2020)
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A.
1/2 CV^2
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B.
CV
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C.
Q^2/2C
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D.
1/2 QV
Solution
The potential energy (U) stored in a capacitor is given by U = 1/2 CV^2.
Correct Answer: A — 1/2 CV^2
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Q. Two capacitors of capacitance 2μF and 3μF are connected in series. What is the equivalent capacitance? (2019)
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A.
1.2μF
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B.
1.5μF
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C.
0.86μF
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D.
5μF
Solution
For capacitors in series, 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/2 + 1/3 = 5/6, giving C_eq = 6/5 = 1.2μF.
Correct Answer: C — 0.86μF
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Q. What happens to the capacitance of a capacitor if a dielectric material is introduced between its plates? (2021)
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A.
Increases
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B.
Decreases
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C.
Remains the same
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D.
Becomes zero
Solution
The capacitance increases when a dielectric material is introduced, as it reduces the electric field between the plates.
Correct Answer: A — Increases
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Q. What is the effect of increasing the area of the plates of a capacitor on its capacitance? (2022)
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A.
Increases capacitance
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B.
Decreases capacitance
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C.
No effect
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D.
Capacitance becomes zero
Solution
Increasing the area A of the plates increases the capacitance, as C = εA/d.
Correct Answer: A — Increases capacitance
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Q. What is the electrostatic potential at a point due to a point charge Q located at a distance r from the charge? (2021)
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A.
kQ/r
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B.
kQr
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C.
kQ/r^2
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D.
kQ^2/r
Solution
The electrostatic potential V at a distance r from a point charge Q is given by V = kQ/r, where k is Coulomb's constant.
Correct Answer: A — kQ/r
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