Q. No.Given below are two statements:
| 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. |
Subtopic: Â Self - Inductance |
 53%
Level 3: 35%-60%
Hints
An inductor \((L)\) and a capacitor \((C)\) are connected in a circuit, with the capacitor initially charged to a maximum voltage \(V_{0}\). The switch is now closed. The maximum current in the circuit is:
| 1. | \( \dfrac{V_{0}}{\sqrt{L C}}\) | 2. | \(V_{0}\sqrt{LC}\) |
| 3. | \(V_{0} \sqrt{\dfrac{L}{C}}\) | 4. | \(V_{0} \sqrt{\dfrac{C}{L}}\) |
Subtopic: Â Self - Inductance |
Level 3: 35%-60%
Hints
The magnetic energy stored in a long current-carrying solenoid, carrying a current of \(2~\text A\) is \(5\times10^{-3}~\text J.\) If the winding is 'doubled' on top of the previous one, and the same current of \(2~\text A\) is passed through both, in the same sense. The stored energy is:
| 1. | \(2.5\times10^{-3}~\text J\) | 2. | \(10\times10^{-3}~\text J\) |
| 3. | \(20\times10^{-3}~\text J\) | 4. | \(80\times10^{-3}~\text J\) |
Subtopic: Â Self - Inductance |
 56%
Level 3: 35%-60%
Hints
Given below are two statements:
| 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. |
Subtopic: Â Self - Inductance |
 60%
Level 2: 60%+
Hints
A time-varying current \(i\) splits into two parts:
(i) \(i_1,\) passing through inductor \(L_1\) and
(ii) \(i_2,\) passing through inductor \(L_2\)
both connected in parallel. Then:
(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. | \(L_1{\Large\frac{di_1}{dt}}=L_2{\Large\frac{di_2}{dt}}\) |
Subtopic: Â Self - Inductance |
 59%
Level 3: 35%-60%
Hints
A coil \((A)\) has an inductance \(L_1\) and a resistance \(R_1,\) while a second coil \((B)\) has an inductance \(L_2,\) but no resistance (or negligible resistance). If these two coils are connected in series, the inductance of the combination will be:
| 1. | \(L_1+L_2\) | 2. | \(L_1\) |
| 3. | \(L_2\) | 4. | \(\sqrt{L_1L_2}\) |
Subtopic: Â Self - Inductance |
 67%
Level 2: 60%+
Hints
A \(3~\mu\text{F}\) capacitor is charged with \(6~\mu \text{C}\) and connected across a \(1~\text{mH}\) inductance. The rate of change of current is:
1. \(2\) A/s
2. \(2\times10^{-3}\) A/s
3. \(2\times10^{3}\) A/s
4. \(2\times10^{-6}\) A/s
1. \(2\) A/s
2. \(2\times10^{-3}\) A/s
3. \(2\times10^{3}\) A/s
4. \(2\times10^{-6}\) A/s
Subtopic: Â Self - Inductance |
 74%
Level 2: 60%+
Hints
Match the quantities in List-I with their appropriate units in List-II.
| 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. | \(\mathrm{A\text-III, B\text{-}IV, C\text-II, D\text- I}\) |
Subtopic: Â Self - Inductance |
 70%
Level 2: 60%+
Hints
Two long solenoids have the same total length and the same total number of turns, but their cross-sectional areas are different: \(A_1,A_2\) where \(A_1>A_2.\) Their self-inductances \(L_1,L_2\) are in the ratio (approximately):
1. \(A_1:A_2\)
2. \(A^2_1:A_2^2\)
3. \(A_2:A_1\)
4. \(A^2_2:A_1^2\)
1. \(A_1:A_2\)
2. \(A^2_1:A_2^2\)
3. \(A_2:A_1\)
4. \(A^2_2:A_1^2\)
Subtopic: Â Self - Inductance |
 80%
Level 1: 80%+
Hints
The self-inductance of a long solenoid of cross-section \(A,\) total length \(L\) and total number of turns \(N,\) is (approximately):
| 1. | \(\dfrac{\mu_0A}{L}\cdot N\) | 2. | \(\dfrac{\mu_0A}{L}\cdot N^2\) |
| 3. | \(\dfrac{\mu_0L^3}{A}\cdot N\) | 4. | \(\dfrac{\mu_0L^3}{A}\cdot N^2\) |
Subtopic: Â Self - Inductance |
 81%
Level 1: 80%+
Hints
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