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Electrostatic Potential and Capacitance Class 12 MCQs Questions with Answers
Question 1.
Dielectric strength of a medium is 2 KV mm-1. What is the maximum potential difference that can be set up across a 50 µm specimen without puncturing it.
(a) 10 V
(b) 100 V
(c) 1000 V
(d) 10,000 V
Answer
Answer: (b) 100 V
Question 2.
A charge q is distributed over two spheres of radii r1 and r2 such that their surface densities are equal. What is the ratio of their potential.
(a) \(\frac {r_1}{r_2}\)
(b) \(\frac {r_1^2}{r_2}\)
(c) \(\frac {U_1^3}{r_2^3}\)
(d) none of these
Answer
Answer: (a) \(\frac {r_1}{r_2}\)
Question 3.
A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the centre of sphere is:
(a) Zero
(b) 10 V
(c) 5 V
(d) \(\frac {10}{3}\) V
Answer
Answer: (b) 10 V
Question 4.
Electric potential V due to an electric dipole is related to the distance r of the observation point as:
(a) V ∝ r
(b) V ∝ r-1
(c) V ∝ r²
(d) V ∝ r-2
Answer
Answer: (d) V ∝ r-2
Question 5.
Two insulated charged spheres of radii 20 cm and 25 cm respectively and having an equal charge q are connected by a copper wire and then they are separated.
(a) Both spheres will have the same charge q.
(b) Charge on sphere of radius 20 cm will be more than that of radius 25 cm.
(c) Charge on sphere of radius 20 cm will be lesser than that of 25 cm.
(d) Charge on each will be zq.
Answer
Answer: (c) Charge on sphere of radius 20 cm will be lesser than that of 25 cm.
Question 6.
A parallel plate air capacitor is given a charge of 3 µC. A sheet of dielectric constant 3 is inserted so that it completely fills the gap between the plates. The induced charge on each face of the sheet is numericaly:
(a) 2 µC
(b) 3 µC
(c) 0
(d) 9 µC
Answer
Answer: (a) 2 µC
Question 7.
Three capacitors of capacitances 3µF, 9µF and 18 µF are conected once in series and then in parallel. The ratio of equivalent capacitances Cs/Cp will be:
(a) 1 : 15
(b) 15 : 1
(c) 1 : 1
(d) 1 : 3
Answer
Answer: (a) 1 : 15
Question 8.
A number of capacitors, each of capacitance 1 µF and each one of which gets punctured if a potential difference just exceeding 500 V is applied are provided. Then an arrangement suitable for giving a capacitor of capacitance 3 µF across which 2000 V may be applied requires at least:
(a) 4 component capacitors.
(b) 48 component capacitors.
(c) 3 component capacitors.
(d) 12 component capacitors.
Answer
Answer: (b) 48 component capacitors.
Question 9.
Five equal capacitors, each with capacitance C are connected as shown. The equivalent capacitance between A and B is.
(a) 5 C
(b) C
(c) C/5
(d) 3C.
Answer
Answer: (b) C
Question 10.
The capacity of an isolated conducting sphere of radius r is proportional to:
(a) r²
(b) \(\frac {1}{r}\)
(c) \(\frac {1}{r^2}\)
(d) r
Answer
Answer: (d) r
Question 11.
Van-de Graff Generator produces a voltage nearly:
(a) 106 V
(b) 108 V
(c) 104 V
(d) none of these.
Answer
Answer: (a) 106 V
Question 12.
The dielectric strength of air at N.T.P. is 3 × 106 V/m. Then the maximum charge that can be given to a spherical conductor of radius 3 m is
(a) 3 × 10-1 C
(b) 3 × 10² V
(c) 3 × 10-3 C
(d) 3 × 10-4 C
Answer
Answer: (c) 3 × 10-3 C
Question 13.
The maximum potential upto which the conductor can be charged in Q12 is
(a) 9 × 105 V
(b) 9 × 106 V
(c) 9 × 107 V
(d) 9 × 108 V.
Answer
Answer: (b) 9 × 106 V
Question 14.
ABC is a right angled ∆ with AB = 3 cm, BC = 4 cm, AB = 5 cm. Charges of +15 stat. C, -12 and 20 stat Coulomb are placed at A, B, C respectively. The electric potential energy of three charges is:
(a) 180 ergs
(b) 4 × 5 × 3 ergs
(c) – 60 ergs
(d) (20 + 15 – 12) ergs.
Answer
Answer: (c) – 60 ergs
Question 15.
The work done in moving the three charges to infinite separation is:
(a) 180 ergs
(b) 60 ergs
(c) – 60 ergs
(d) (20 + 15 -12) ergs.
Answer
Answer: (b) 60 ergs
Fill in the Blanks
Question 1.
The charge on the earth cannot be neutralized because ………………..
Answer
Answer:
Lightning and thunder storms are the continuous phenomenon all over the world which send a charge equal to 1800 C per second into the earth and hence – 5 × 105 C charge is maintained on earth.
Question 2.
A potential difference of the order or ……………….. is created between the earth and the bottom of the cloud.
Answer
Answer: 108 V.
Question 3.
The top of ……………….. and the surface of the earth form a spherical capacitor of capacitance ………………..
Answer
Answer: Stratosphere, 0.09 F (= 0.1 F).
Question 4.
Force between the plates of a capacitor is ……………….. which varies ……………….. as the area of the plates and is independent of the ………………..
Answer
Answer: \(\frac {1}{2}\), \(\frac {q^2}{ε_0KA}\), inversely, separation between the plates.
Question 5.
When a dielectric slab is introduced by disconnecting the battery from the capacitor, then q = ………………..
V = ………………..
σ = ………………..
E = ………………..
U = ………………..
C = ………………..
Answer
Answer:
q = q0
σ = σ0
E = \(\frac {V_0}{K}\)
U = \(\frac {U_0}{K}\)
C = KC0.
Question 6.
If the medium surrounding the conductor is charged, then the potential of the conductor is ………………..
Answer
Answer: Changed.
Question 7.
If at any point E = 0, then V may or may not be ……………….. e.g. inside a charged conductor E = ……………….. but V is ………………..
Answer
Answer: Zero, Zero, not zero.
Question 8.
Electric potential at a point on the equitorial line of a dipole is ……………….. but \(\vec{E}\) is ………………..
Answer
Answer: Zero, not equal to zero.
Question 9.
Two equipotential surfaces cannot intersect each other because ………………..
Answer
Answer: Then there will be two values of electric potential at that point which is impossible.
Question 10.
Energy of an electric dipole is minimum when ………………..
Answer
Answer: It is aligned with the direction of the electric field.
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