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Q. No.The capacitance of the system of three parallel plates of plate area \(A,\) plate separation \(d\) is measured between the center plate \((X)\) and the two outer plates \((Y)\) connected together. It is equal to:
1. \(\dfrac{2\varepsilon_0A}{d}\)
2. \(\dfrac{\varepsilon_0A}{2d}\)
3. \(\dfrac{\varepsilon_0A}{d}\)
4. \(\dfrac{4\varepsilon_0A}{d}\)
Subtopic: Capacitance |
68%
Level 2: 60%+
Hints
A non-conducting circular plate is uniformly charged and the potential at its center is \(V_0.\) If all the charge is collected and kept at its edge, then the potential will be:
| 1. | \(2V_0\) | 2. | \(\dfrac{V_0}{2}\) |
| 3. | \(\dfrac{V_0}{3}\) | 4. | \(\dfrac{V_0}{\sqrt2}\) |
Subtopic: Electric Potential |
53%
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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. \(\dfrac{5C}{2}\)
1. \(2C\)
2. \(\dfrac{3C}{2}\)
3. \(3C\)
4. \(\dfrac{5C}{2}\)
Subtopic: Combination of Capacitors |
66%
Level 2: 60%+
Hints
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. \(\dfrac{-mgR}{\sqrt2}\)
1. \(-MgR\)
2. \(-mgR\)
3. \(\dfrac{-MgR}{\sqrt2}\)
4. \(\dfrac{-mgR}{\sqrt2}\)
Subtopic: Electric Potential Energy |
Level 3: 35%-60%
Hints
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%
Level 2: 60%+
Hints
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 |
Level 3: 35%-60%
Hints
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 |
Level 4: Below 35%
Hints
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
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 |
51%
Level 3: 35%-60%
Hints
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
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%
Level 2: 60%+
Hints
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