Q. No.An uncharged capacitor \((C)\) is connected to a battery of emf \(E\). Once it is fully charged, it is connected to a second battery of emf \(2E\). The positive terminal of the capacitor and battery are connected and their negative terminals are similarly connected together. The energy dissipated as heat, when the second battery is connected is:
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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| (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. | \(\dfrac{K\varepsilon_0\pi r^2}{d}\) | 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. |
| (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. \(W_1=W_2\)
2. \(2W_1 =W_2\)
3. \(W_1 = 2W_2\)
4. \(4W_1 = W_2\)
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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. | \(2 \hat{i}+\hat{j}\) | 2. | \(2 \hat{j}+\hat{i}\) |
| 3. | \(\dfrac{1}{4} \hat{i}+\hat{j}\) | 4. | \( \dfrac{1}{4} \hat{j}+\hat{i}\) |
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The capacitance is now \(C_2.\)
\(\dfrac{C_1} { C_2}\) equals:
| 1. | \(3\) | 2. | \(2\) |
| 3. | \(\dfrac{3}{2}\) | 4. | \(\dfrac{4}{3}\) |
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