Q. No.| Assertion (A): | When emf is induced in a circuit due to a changing magnetic field, it is essential that the field is produced by another circuit - i.e. the field produced by the current in the same circuit cannot induce an emf in itself. |
| Reason (R): | Faraday's Law of electromagnetic induction requires that the rate of change of magnetic flux through the circuit equals the emf. |
| 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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| 1. | \( \dfrac{V_{0}}{\sqrt{L C}}\) | 2. | \(V_{0}\sqrt{LC}\) |
| 3. | \(V_{0} \sqrt{\dfrac{L}{C}}\) | 4. | \(V_{0} \sqrt{\dfrac{C}{L}}\) |
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| 1. | \(2.5\times10^{-3}~\text J\) | 2. | \(10\times10^{-3}~\text J\) |
| 3. | \(20\times10^{-3}~\text J\) | 4. | \(80\times10^{-3}~\text J\) |
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| Statement I: | The magnetic field due to a very long current-carrying solenoid, at its centre, is inversely proportional to the radius of the solenoid, other things remaining constant. |
| Statement II: | The magnetic energy stored in a solenoid carrying a current \(I\) is directly proportional to \(I^2.\) |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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(i) \(i_1,\) passing through inductor \(L_1\) and
(ii) \(i_2,\) passing through inductor \(L_2\)
both connected in parallel. Then:
| 1. | \(L_1{\Large\frac{di_1}{dt}}+L_2{\Large\frac{di_2}{dt}}=\text{constant}\) |
| 2. | \({\Large\frac{1}{L_1}\frac{di_1}{dt}}+{\Large\frac{1}{L_2}\frac{di_2}{dt}}=\text{constant}\) |
| 3. | \({\Large\frac{1}{L_1}\frac{di_1}{dt}}={\Large\frac{1}{L_2}\frac{di_2}{dt}}\) |
| 4. | \(L_1{\Large\frac{di_1}{dt}}=L_2{\Large\frac{di_2}{dt}}\) |
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| 1. | \(L_1+L_2\) | 2. | \(L_1\) |
| 3. | \(L_2\) | 4. | \(\sqrt{L_1L_2}\) |
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1. \(2\) A/s
2. \(2\times10^{-3}\) A/s
3. \(2\times10^{3}\) A/s
4. \(2\times10^{-6}\) A/s
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| List-I | List-II | ||
| (A) | inductance \(\times\) current | (I) | V |
| (B) | frequency \(\times\) capacitance | (II) | Wb |
| (C) | frequency \(\times\) magnetic flux | (III) | \(\Omega^{-1}\) |
| (D) | electric flux | (IV) | V-m |
| 1. | \(\mathrm{A\text-I, B\text{-}IV, C\text-II, D\text- III}\) |
| 2. | \(\mathrm{A\text-II, B\text{-}III, C\text-I, D\text- IV}\) |
| 3. | \(\mathrm{A\text-III, B\text{-}I, C\text-II, D\text- IV}\) |
| 4. | \(\mathrm{A\text-III, B\text{-}IV, C\text-II, D\text- I}\) |
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1. \(A_1:A_2\)
2. \(A^2_1:A_2^2\)
3. \(A_2:A_1\)
4. \(A^2_2:A_1^2\)
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| 1. | \(\dfrac{\mu_0A}{L}\cdot N\) | 2. | \(\dfrac{\mu_0A}{L}\cdot N^2\) |
| 3. | \(\dfrac{\mu_0L^3}{A}\cdot N\) | 4. | \(\dfrac{\mu_0L^3}{A}\cdot N^2\) |
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