The equivalent capacitance of the circuit between the points \(A~\text{and}~B\) is equal to:

           
1. \(2C\)

2. \(\dfrac{3C}{2}\)

3. \(3C\)

4. \(\dfrac{5C}{2}\)

Subtopic:  Combination of Capacitors |
 66%
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A particle \((P)\) of mass \(m\) is placed on the axis of a uniform circular ring of radius \(R\) and mass \(M.\) Its distance \((OP)\) from the centre \((O)\) of the ring is equal to \(R.\) Let the net gravitational field at the centre of the ring be \(g.\) Then, the gravitational potential energy of the interaction of the system is:
         

1. \(-MgR\)
2. \(-mgR\)
3. \(\dfrac{-MgR}{\sqrt2}\)
4. \(\dfrac{-mgR}{\sqrt2}\)
Subtopic:  Electric Potential Energy |
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A uniformly charged metallic sphere holds a total charge \(Q_0\) and has a potential \(V_0.\) The total potential energy stored is:
1. \(Q_0V_0\) 2. \(\dfrac{Q_0V_0}{2}\)
3. \(\dfrac{Q_0V_0}{4}\) 4. \(-Q_0V_0\)
Subtopic:  Electric Potential Energy |
 62%
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Two concentric metallic spheres, surface areas \(A_1,A_2\) and separation \(d\), have a capacitance \(C_0.\) If a parallel plate capacitor is built with the same separation \(d,\) and has the same capacitance \(C_0\) then its plate area will be:
1. \(\dfrac{A_1+A_2}{2}\) 2. \(\sqrt{A_1A_2}\)
3. \(\dfrac{2A_1A_2}{A_1+A_2}\) 4. \(\dfrac{A_1^2A_2^2}{A_1+A_2}\)
Subtopic:  Capacitance |
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Identical charges are distributed uniformly on the surfaces of a sphere and a disc of the same radius. The potential at the centre of the sphere is \(V_1,\) and the potential at the centre of the disc is \(V_2.\) The ratio \(\dfrac{V_2}{V_1}\) will be equal to:
1. \(1\) 2. \(2\)
3. \(4\) 4. \(\sqrt2\)
Subtopic:  Electric Potential |
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The circuit shown in the diagram given below, is set up with all the capacitors initially uncharged.
                       
The potential difference between \(A\) and \(B\) when \(A\) is connected to \(X\) and \(B\) is connected to \(Y,\) is:
1. \(2.6\) V 
2. \(2.4\) V 
3. \(6\) V 
4. zero
Subtopic:  Capacitance |
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The circuit shown in the diagram given below, is set up with all the capacitors initially uncharged.
                     
The potential difference between \(A\) and \(B,\) after \(A\) is connected to \(Y\) and \(B\) to \(X,\) is:
1. \(2.6\) V
2. \(2.4\) V
3. \(6\) V
4. zero
Subtopic:  Capacitance |
 62%
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A charge is uniformly distributed on the circumference of a disc, and the potential at its centre is \(5\) volt. If the charge was uniformly distributed on the surface of this disc, the potential at a point \(P\) on its axis, at a distance equal to the disc's radius from its centre, equals:
1. \(10\) V
2. \(5 \sqrt 2\) V
3. \(10 \sqrt 2\) V
4. \(10 (\sqrt {2} -1)\) V
Subtopic:  Electric Potential |
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A negative point charge \((-q)\) is placed at the centre of a spherical ball of charge distributed uniformly over its volume. The radius of the ball is \(R.\) The electric field on its surface is zero. The potential on its surface is:
1. zero 2. \(\dfrac{kq }{2R}\)
3. \(\dfrac{-kq }{ 2R}\) 4. \(\dfrac{2kq }{ R}\)
Subtopic:  Electric Potential |
 62%
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A capacitance is formed by connecting two metallic balls of radius \(r\) by a conducting wire, and two oppositely charged identical metallic hemispheres \((A,B)\) slightly larger than the balls. The separation between the hemispheres and the respective balls is \(d.\) The capacitance between \(A,B\) is:
1. \(\dfrac{4\pi\varepsilon_0r^2}{d}\) 2. \(\dfrac{2\pi\varepsilon_0r^2}{d}\)
3. \(\dfrac{\pi\varepsilon_0r^2}{d}\) 4. \(\dfrac{\pi\varepsilon_0r^2}{2d}\)
Subtopic:  Capacitance |
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