Q. No.Three concentric spherical conducting shells of radii \(a,b,\) and \(c~(a<b<c)\) are placed as shown. Let \(C_{ab}\) be the capacitance when \(a\) and \(b\) spheres are charged with \(+Q,-Q\) and similarly, let \(C_{bc}\) be the capacitance between \(b\) and \(c\) spheres while \(C_{ac}\) be the capacitance between \(a\) and \(c\) sphere. Then:
1. \(C_{ab}+C_{bc}=C_{ac}\)
2. \(\dfrac{1}{C_{ab}}+\dfrac{1}{C_{bc}}=\dfrac{1}{C_{ac}}\)
3. \(\sqrt{C_{ab}\cdot C_{bc}}=C_{ac}\)
4. \(C_{ab}-C_{bc}=C_{ac}\)
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1. increases by \(20\)%
2. decreases by \(20\)%
3. increases by \(33\)%
4. decreases by \(25\)%
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1. \(\dfrac{Q^2}{4\pi\varepsilon_0R}\)
2. \(\dfrac{2Q^2}{4\pi\varepsilon_0R}\)
3. \(\dfrac12 \left ( \dfrac{Q^2}{4\pi\varepsilon_0R} \right )\)
4. \(\dfrac{Q^2}{16\pi\varepsilon_0R}\)
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1. \(W_1=W_2\)
2. \(2W_1 =W_2\)
3. \(W_1 = 2W_2\)
4. \(4W_1 = W_2\)
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| (I) | The charge on the plates. |
| (II) | The potential difference between the plates. |
| (III) | The energy stored in the capacitor. |
Choose the correct option from given ones:
| 1. | (I) only | 2. | (I) and (II) |
| 3. | (I) and (III) | 4. | (I), (II) and (III) |
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| 1. | \(\dfrac{K\varepsilon_0\pi r^2}{d}\) | 2. | \(\dfrac{K\varepsilon_0\pi r^2}{2d}\) |
| 3. | \(\dfrac{K+1}{2}\dfrac{\varepsilon_0\pi r^2}{d}\) | 4. | None of the above |
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| (I) | The charge on the plates increases. |
| (II) | The energy stored in the capacitor increases. |
| (III) | Work is done by the battery as the slab is inserted. |
Choose the correct answer from the options given below:
| 1. | (I), and (II) are True. |
| 2. | (I) and (III) are True. |
| 3. | only (I) is True. |
| 4. | (I), (II), and (III) are True. |
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| 1. | \(\dfrac{3}{2}CE^2\) | 2. | \(\dfrac{1}{2}CE^2\) |
| 3. | \(CE^2\) | 4. | \(\dfrac{5}{2}CE^2\) |
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1. \(1.5~\mu\text{C}\)
2. \(3~\mu\text{C}\)
3. \(4.5~\mu\text{C}\)
4. \(9~\mu\text{C}\)
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Given below are two statements:
| Assertion (A): | The electric flux due to the external charge \(q\) and the induced charges on the sphere through the spherical surface \(S\) shown dotted in the diagram, is \(\left(-\dfrac{q}{\varepsilon_0}\right)\). |
| Reason (R): | Negative charges are induced on the surface of the conducting sphere due to the positive charge \(q\) in the vicinity, and the potential of the conducting sphere is zero. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
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