Capacitance(12th Grade > Physics ) Questions and answers for exam Preparation

12th Grade > Physics

CAPACITANCE MCQs

Total Questions : 26 | Page 3 of 3 pages

Question 21. Between the plates of a parallel plate capacitor a dielectric plate is introduced just to fill the space between the plates. The capacitor is charged and later disconnected from the battery. The dielectric plate is slowly drawn out of the capacitor parallel to the plates. The plot of the potential difference across the plates and the length of the dielectric plate drawn out is

Discuss Question

Answer: Option A. ->
:
B
While drawing the dielectric plate outside, the capacitance decreases till the entire plate comes out and then becomes constant. So, V increases and then becomes constant.

Question 22. A capacitor is charged by using a battery which is then disconnected. A dielectric slab is then slipped between the plates, which results in:

Reduction of charge on the plates and increase of potential across the plates
Increase in the potential difference across the plates,reduction in stored energy, but no change in the charge on the plates
Decrease in the potential difference across the plates reduction in stored energy, but no change in the charge on the plates
None of the above

Discuss Question

Answer: Option C. -> Decrease in the potential difference across the plates reduction in stored energy, but no change in the charge on the plates
:
C
The charge on the plates does not change as the capacitor is disconnected from the battery. The presence of dielectric slab increases the capacitance, which decreases the potential difference. Thus, the energy stored is reduced.

Question 23. The capacities of the three capacitors are in ratio 1 : 2 : 3. Their equivalent capacity when connected in parallel is

\frac{60}{11} μ F

more than when they are connected in series. The individual capacities of capacitors in

μ F

are?

4, 6, 7
1, 2, 3
2, 3, 4
1, 3, 6

Discuss Question

Answer: Option B. -> 1, 2, 3
:
B

C_{p} = x + 2 x + 3 x = 6 x - - - - - (1)

\frac{1}{C_{s}} = \frac{1}{x} + \frac{1}{2 x} + \frac{1}{3 x} = \frac{11}{6 x}

C_{s} = \frac{6 x}{11} - - - - - - - - (2)

C_{p} = \frac{60}{11} + C s

6 x = \frac{60}{11} + \frac{6 x}{11}

66 x - 6 x = 60

60 x = 60 x = 1 μ F

C_{1} = 1 μ F; C_{2} = 2 μ F; C_{3} = 3 μ F

Question 24. The energy stored in a condenser of capacity C which has been raised to a potential V is given by

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Answer: Option B. -> 1, 2, 3
:
B

Question 25. A parallel plate condenser with plate separation ‘d’ and plate area A is connected to a battery and charged to a potential V. Then the battery is disconnected and with insultated handles the plate separation is increased to 2d. Work done in the process will be?

ϵ0A4dV2
ϵ0AdV2
ϵ0A2dV2
2ϵ0AdV2

Discuss Question

Answer: Option C. -> ϵ0A2dV2
:
C

U_{1} = \frac{1}{2} \frac{Q^{2}}{c} - - - - - - - (1)

U_{2} = \frac{1}{2} \frac{Q^{2}}{c_{1}} = \frac{1}{2} \frac{Q^{2}}{\frac{c}{2}} = \frac{Q^{2}}{c} - - - - - (2)

W = U_{2} - U_{1}, = \frac{1}{2} \frac{Q^{2}}{c} [2 - 1]

= \frac{1}{2} \frac{C^{2} V^{2}}{c} = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{ϵ_{0} A}{d} V^{2}

Question 26. A capacitor stores charge Q at a potential difference V. If the voltage applied by a battery to the capacitor is doubled to 2V, then

The capacitance falls to half its initial value and the charge remains the same
The capacitance and the charge both fall to half their initial values
The capacitance and the charge both double
The capacitance remains the same and the charge doubles

Discuss Question

Answer: Option D. -> The capacitance remains the same and the charge doubles
:
D
The capacitance for a given system is a constant and is independent of charge as well as potential. As