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

           
1. \(2C\)
2. \(\frac{3C}{2}\)
3. \(3C\)
4. \(\frac{5C}{2}\)

Subtopic:  Combination of Capacitors |
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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. \({kq \over 2R}\)
3. \({-kq \over 2R}\)
4. \({2kq \over R}\)
Subtopic:  Electric Potential |
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Four charges \(q,q\) and \(-q,-q\) are placed at the four vertices of a square of side \(a,\) with like charges across a diagonal. The potential at the centre of the square is:
1. zero
2. \(\sqrt2\frac{kq}{a}\)
3. \(2\frac{kq}{a}\)
4. \(4\frac{kq}{a}\)
Subtopic:  Electric Potential |
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The angle between the electric lines of force and the equipotential surface is: 
1. \(180^\circ\)
2. \(0^\circ\)
3. \(45^\circ\)
4. \(90^\circ\)
Subtopic:  Equipotential Surfaces |
 82%
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Four particles having identical charges are placed at the four corners of a square of side \(2\) m. The potential at the centre of the square is \(2\sqrt2\)  V.
The potential energy of the system of charges is \(U_0.\) If the charges are brought closer so that each side of the square is \(1\) m, then the new potential energy of the system will be:
1. \(U_0\) 2. \(\frac{U_0}{2}\)
3. \(2U_0\) 4. \(4U_0\)
Subtopic:  Electric Potential Energy |
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The capacitance of a system of concentric conducting spherical shells is \(2~\mu\text F.\) If the radii of both the shells are doubled, then the capacitance of the system will be:
1. \(8~\mu\text F\)
2. \(4~\mu\text F\)
3. \(1~\mu\text F\)
4. \(0.5~\mu\text F\)
Subtopic:  Capacitance |
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The left plate \(A\) of an air capacitor is connected to the positive terminal while the right plate \(B\) is connected to the negative terminal of a cell of voltage \(V_0.\) Assume that the plate area is \(A,\) and the plate separation is \(d.\) If a slab of dielectric constant \(K\) is inserted into the space between the plates, the electric field in the dielectric will be: (compared to the air capacitor)
                   
 
1. more.
2. less.
3. equal.
4. more or less or equal depending on the value of \(K\).
Subtopic:  Dielectrics in Capacitors |
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A dipole (\(p\)) is placed so that it is always aligned along the x-axis but it can undergo displacement along the x-axis. The dipole is placed exactly midway between two fixed charges \(-Q\) and \(Q,\) in two possible ways.
                            
Then, the dipole is:
1. stable in both A, B
2. stable in A, unstable in B
3. unstable in A, stable in B
4. unstable in both A, B
Subtopic:  Energy of Dipole in an External Field |
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A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities will remain the same?

(a) the electric field in the capacitor
(b) the charge on the capacitor
(c) the potential difference between the plates
(d) the stored energy in the capacitor

 
Choose the correct option:
1. (a), (b)
2. (b) only
3. (c), (a)
4. (a), (d)

Subtopic:  Dielectrics in Capacitors |
 78%
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