Capacitance(11th And 12th > Physics ) Questions and answers for exam Preparation

Question 1.

In an adjoining figure are shown three capacitors C₁,C₂ and C₃ joined to a

battery. The correct condition will be (Symbols have their usual meanings)

Explanation:-

Answer: Option C. ->

:
C

Q₁=Q₂+Q₃ because in series combination charge is same on both the

condenser and V=V₁+V₂ because in parallel combination V₂=V₃

Hence V=V₁+V₂

Question 2.

If two conducting spheres are separately charged and then brought in contact, then

The total energy of the two spheres is conserved
The total charge on the two spheres is conserved
Both the total energy and charge are conserved
The final potential is always the mean of the original potentials of the two spheres

Explanation:-

Answer: Option B. -> The total charge on the two spheres is conserved
:
B

The total charge on the spheres will be conserved

Question 3.

In a charged capacitor, the energy resides as

Positive charges
Both the positive and negative charges
The field between the plates
Around the edge of the capacitor plates

Explanation:-

Answer: Option C. -> The field between the plates
:
C
In a charged capacitor energy is stored in the form electric field

Question 4.

When a dielectric slab is introduced between the plates of an isolated charged capacitor, it

Increase the capacitance of the capacitor
Decreases the electric filed between the plates
Decreases the amount of energy stored in the capacitor
All of the above

Explanation:-

Answer: Option D. -> All of the above
:
D

As the capacitor is isolated, the potential decreases as the capcitance increases

Question 5.

The insulated metal spheres of radii R₁ and R₂ having charges Q₁ and Q₂ respectively are connected to each other. There is

No change in the energy of the system
An increase in the energy of the system
Always a decrease in the energy of the system
A decrease in the energy of the system unless Q₁R₂=Q₂R₁

Explanation:-

Answer: Option D. -> A decrease in the energy of the system unless Q₁R₂=Q₂R₁
:
D

When Potentials of spheres are unequal, current will flow in connecting wire so that energy decreases in the form of heat through the connecting wire.

Question 6.

A certain number of identical condensers are first connected in series and then in parallel. If the equivalent capacities in the two cases are found to be in the ratio 1: 9, what is the number of condensers?

9
3
27
81

Explanation:-

Answer: Option B. -> 3
:
B

\frac{C_{s} e r i e s}{C_{p} a r a l l e l} = \frac{(\frac{C}{n})}{n c} = \frac{1}{n^{2}}

\frac{1}{9} = \frac{1}{n^{2}}

n = 3

Question 7.

A conducting sphere of radius R, and carrying a charge q is joined to a conducting sphere of radius 2R, and carrying a charge – 2q. The charge flown between them will be?

$\frac{q}{3}$
$\frac{2 q}{3}$
$q$
$\frac{4 q}{3}$

Explanation:-

Answer: Option D. ->

\frac{4 q}{3}

:
D
Initial charge on sphere of radius R = q
Charge on this sphere after joining

= q^{'} = \frac{R q + (- 2 q) \times R}{R + 2 R} = \frac{- q \times R}{3 R} = \frac{- q}{3}

So charge flown between them

= q - (- \frac{q}{3}) = \frac{4 q}{3}

Question 8.

A parallel plate air condenser has a capacity ‘C’. When the plate separation is halved and a dielectric of constant k is inserted, new capacitance is found to be 12C. The value of dielectric constant ‘k’ is?

12
24
6
3

Explanation:-

Answer: Option C. -> 6
:
C

C = \frac{ϵ_{0} A}{d}; C^{1} = \frac{k ϵ_{0} A}{(\frac{d}{2})}

\frac{C^{1}}{C} = 2 k;

12 = 2 k; k = \frac{12}{2} = 6

Question 9.

A capacitor 1mF withstands a maximum voltage of 6KV, while another capacitor 2mF withstands a maximum voltage of 4KV. If the capacitors are connected in series, the system will withstand a maximum voltage of?

2 KV
4 KV
6 KV
9 KV

Explanation:-

Answer: Option D. -> 9 KV
:
D

q_{1} = C_{1} V_{1} = 10^{- 3} \times 6 \times 10^{3} = 6 C

q_{1} = C_{2} V_{2} = 2 \times 10^{- 3} \times 4 \times 10^{3} = 8 C

Q = q_{1} = 6 C Q = C V

6 = (\frac{C_{1} C_{2}}{C_{1} + C_{2}}) V

6 = \frac{2}{3} \times 10^{- 3} V

V = 9 \times 10^{3} V

= 9 K V

Question 10.

In the circuit given below potential difference across 6 $μ$ F capacitor is

8 V
4 V
6 V
3 V

Explanation:-

Answer: Option B. -> 4 V
:
B

q = C_{1} V_{1} = C^{1} V_{2}

\frac{V_{1}}{V_{2}} = \frac{C^{1}}{C_{1}} = \frac{9}{4.5} = \frac{2}{1}

\frac{V_{1} + V_{2}}{V_{2}} = \frac{2 + 1}{1}

V_{2} = \frac{12}{3} = 4 V