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Q. No.An inductor \((L)\) and a resistor \((R)\) are connected in series and a battery is connected, as shown in the figure. Once the current becomes steady, the power in the resistance is \(P_R\) and the energy stored in the inductor is \(U_L.\) The switch is suddenly (and smoothly) toggled to the position \(B\) allowing the inductor to discharge. The time in which the energy stored becomes \(\dfrac12\) its initial value is:
1.
\(\dfrac{U_L}{P_R}\)
2.
\(\dfrac{U_L~\mathrm {ln}2}{P_R}\)
3.
\(\dfrac{2U_L~\mathrm{ln 2}}{P_R}\)
4.
\(\dfrac{2U_L}{P_R}\)
Subtopic: LR circuit |
54%
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A circular wire of radius \(R\) is placed in a uniform magnetic field \(B,\) which acts into the plane as shown. The wire is given a half-turn about a diameter. The resistance per unit length of the wire is \(\lambda.\) The total charge flowing through the wire is:
| 1. | \(\dfrac{2BR}{\lambda}\) | 2. | \(\dfrac{BR}{\lambda}\) |
| 3. | \(\dfrac{BR}{2\lambda}\) | 4. | zero |
Subtopic: Motional emf |
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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: Self - Inductance |
81%
From NCERT
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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. | \(2\sqrt{\dfrac{L}{C}}\) |
Subtopic: LR circuit |
58%
From NCERT
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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: Self - Inductance |
72%
From NCERT
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A conducting circular wire of radius \(r\) is moving with constant velocity \(v\) towards the right in a uniform magnetic field \(B.\) We consider two points \(X,Y\) such that chord \(XY\) is perpendicular to the velocity \(v\) and is at a distance \(x\) from the centre \((O)\) of the circle. The EMF induced between \(X,Y\) is \(\varepsilon.\) Then, \(\varepsilon\) is proportional to:
1. \(x\)
2. \(\sqrt{r^2-x^2}\)
3. \(r\)
4. \(x\sqrt{r^2-x^2}\)
1. \(x\)
2. \(\sqrt{r^2-x^2}\)
3. \(r\)
4. \(x\sqrt{r^2-x^2}\)
Subtopic: Motional emf |
73%
From NCERT
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Given below are two statements:
| 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). |
Subtopic: Faraday's Law & Lenz Law |
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An \(L\)-shaped rod \((ABC;AB=BC=a)\) moves in its own plane with a velocity \(v\) parallel to \(AB.\) There is a uniform magnetic field \(B\) acting into the plane as shown. The emf developed between \(A,C\) is:
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
Subtopic: Motional emf |
57%
From NCERT
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Given below are two statements:
| 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). |
Subtopic: Faraday's Law & Lenz Law |
67%
From NCERT
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The magnetic field, through a closed loop of conducting wire covering an area of \(100\) cm2, is \(5\times10^{-2}\) T and it is uniform and normal to the area. If the field is switched off in a time of \(10\) ms, the average EMF induced is:
| 1. | \(5\) V | 2. | \(0.5\) V |
| 3. | \(0.05\) V | 4. | \(5\times10^{-4}\) V |
Subtopic: Faraday's Law & Lenz Law |
78%
From NCERT
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