Q. No.The \(\text{DC}\) time constant of an \(L\)-\(R\) circuit is the same as that of an \(R\)-\(C\) circuit where the inductor in the first circuit was replaced by a capacitor. The value of the resistance \(R\) equals:
1.
\(\dfrac{1}{2\pi}\sqrt{\dfrac{L}{C}}\)
2.
\(\sqrt{\dfrac{L}{C}}\)
3.
\(2\pi\sqrt{\dfrac{L}{C}}\)
4.
\(2\sqrt{\dfrac{L}{C}}\)
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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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1. \(x\)
2. \(\sqrt{r^2-x^2}\)
3. \(r\)
4. \(x\sqrt{r^2-x^2}\)
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| Assertion (A): | Faraday's law of electromagnetic induction is a consequence of Biot-Savart's law. |
| Reason (R): | Currents cause magnetic fields and interact with magnetic flux. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
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1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
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| Assertion (A): | Faraday's law of electromagnetic induction is not consistent with the law of conservation of energy. |
| Reason (R): | Lenz's law is consistent with energy conservation. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
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| 1. | \(5\) V | 2. | \(0.5\) V |
| 3. | \(0.05\) V | 4. | \(5\times10^{-4}\) V |
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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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| List-I | List-II | ||
| \((\mathrm{A})\) | inductance \(\times\) current | \((\mathrm{I})\) | V |
| \((\mathrm{B})\) | frequency \(\times\) capacitance | \((\mathrm{II})\) | Wb |
| \((\mathrm{C})\) | frequency \(\times\) magnetic flux | \((\mathrm{III})\) | \(\Omega^{-1}\) |
| \((\mathrm{D})\) | electric flux | \(\mathrm{IV}\) | 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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| Statement I: | A steady magnetic field can be produced by a steady current. |
| Statement II: | A steady current can be produced in a circuit by a changing magnetic field. |
| 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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