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1.

The equivalent capacitance between A and B is as the given figure:

1. \(16 \pi \epsilon_ 0 r\)
2. \(4 \pi \epsilon_ 0 r\)
3. \(8 \pi \epsilon_ 0 r\)
4. None of these

2.

In the circuit shown in figure, energy stored in \(6~\mu\text{F}\) capacitor will be:
   

1.	\(48 \times10^{-6}~\text{J}\)	2.	\(32 \times10^{-6}~\text{J}\)
3.	\(96 \times10^{-6}~\text{J}\)	4.	\(24 \times10^{-6}~\text{J}\)

3.

Two identical metal plates are given charges $Q_1 and Q_2\left(<Q_1\right)$ respectively. If they are now brought close to form a parallel plate capacitor with capacitance $C$, the potential difference between them is :
1. $\frac{Q_1+Q_2}{2C}$
2. $\frac{Q_1+Q_2}{C}$
3. $\frac{Q_1-Q_2}{C}$
4. $\frac{Q_1-Q_2}{2C}$

4.

The capacity of parallel plate condenser depends on 
(1) The type of metal used
(2) The thickness of plates
(3) The potential applied across the plates
(4) The separation between the plates

5.

If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).

6.

A spherical condenser has inner and outer spheres of radii a and b respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed respectively will be 
(1) Zero
(2) $4\pi {\epsilon }_{0}a$
(3) $4\pi {\epsilon }_{0}b$
(4) $4\pi {\epsilon }_{0}a\left(\frac{{\displaystyle b}}{{\displaystyle b-a}}\right)$

7.

Two insulated metallic spheres of 3 μF and 5 μF capacitances are charged to 300 V and 500V respectively. The energy loss, when they are connected by a wire is 
(1) 0.012 J
(2) 0.0218 J
(3) 0.0375 J
(4) 3.75 J

8. A parallel plate capacitor of capacity \(C_0\) is charged to a potential \(V_0\)
(i) The energy stored in the capacitor when the battery is disconnected and the separation is doubled is \(E_1\)
(ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is \(E_2\).
Then \(\frac{E_1}{E_2}\) value is:
1. \(4\)
2. \(\frac{3}{2}\)
3. \(2\)
4. \(\frac{1}{2}\)

9.

Four plates of equal area A are separated by equal distances d and are arranged as shown in the figure. The equivalent capacity is

(1) $\frac{2{\epsilon }_{0}A}{d}$
(2) $\frac{3{\epsilon }_{0}A}{d}$
(3) $\frac{4{\epsilon }_{0}A}{d}$
(4) $\frac{{\epsilon }_{0}A}{d}$

10.

Three capacitors are connected to D.C. source of 100 volts shown in the adjoining figure. If the charge accumulated on plates of C₁, C₂ and C₃ are $q_a,q_b,q_c,q_d.q_e$ and q_f respectively, then 

(1) $q_b+q_d+q_f=\frac{100}{9}C$
(2) $q_b+q_d+q_f=0$
(3) $q_a+q_c+q_e=50C$
(4) $q_b=q_d=q_f$

11.

A capacitor of capacity C₁ is charged to the potential of V₀. On disconnecting with the battery, it is connected with a capacitor of capacity C₂ as shown in the adjoining figure. The ratio of energies before and after the connection of switch S will be

(1) (C₁ + C₂)/C₁
(2) C₁/(C₁ + C₂)
(3) C₁C₂
(4) C₁/C₂

12.

In the adjoining figure, four capacitors are shown with their respective capacities and the P.D. applied. The charge and the P.D. across the 4 μF capacitor will be

(1) 600 μC; 150 volts
(2) 300 μC; 75 volts
(3) 800 μC; 200 volts
(4) 580 μC; 145 volts

13.

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system 
1. increases by a factor of 4
2.decreases by a factor of 2
3. remain the same 
4. increases by a factor of 2

14.

A parallel-plate capacitor of area A, plate separation d, and capacitance C is filled with four dielectric materials having dielectric constants $k_1,k_2,k_3$ $$and $k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by
       
(a) $\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$
(b) $k=\frac{2}{3}\left(k_1+k_2+k_3\right)+2k_4$
(c) $\frac{1}{k}=\frac{3}{2\left(k_1+k_2+k_3\right)}+\frac{1}{2k_4}$
(d) $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

15.

A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \(S\) is turned to position \(2\), the percentage of its stored energy dissipated is:
         

1.	\(20\%\)	2.	\(75\%\)
3.	\(80\%\)	4.	\(0\%\)

16.

A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is
(1)C²V²/2d

(2)CV²/2d

(3)CV²/d

(4)C²V²/2d²

17.

Two thin dielectric slabs of dielectric constants K₁&K₂ ($K_1<K_2$) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by  

1.
2. 
3.
4.

18.

Two metallic spheres of radii \(1\) cm and \(3\) cm are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2}~\text{C},\) respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:
1. \(2\times 10^{-2}~\text{C}\)
2. \(3\times 10^{-2}~\text{C}\)
3. \(4\times 10^{-2}~\text{C}\)
4. \(1\times 10^{-2}~\text{C}\)

19.

A 10 μF capacitor and a 20 μF capacitor are connected in series across a 200 V supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor 
(1) $\frac{400}{9}V$
(2) $\frac{800}{9}V$
(3) 400 V
(4) 200 V

20.

To form a composite 16 μF, 1000 V capacitor from a supply of identical capacitors marked 8 μF, 250 V, we require a minimum number of capacitors
1. 40
2. 32
3. 8
4. 2