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Q. No.A rectangular loop of conducting wire is bent symmetrically so that its two plane halves are inclined at right angles with respect to each other (i.e. \(\angle { PQR }=\angle S T U=90^{\circ}\)). Every segment has a length '\(a\)' \((PQ=QR=RS=...=UP=a)\). A uniform time-dependent magnetic field \(B(t)\) acts on the loop, making an angle '\(\alpha\)' with the lower half of the loop and '\(90^o - \alpha \)' with the upper half. The EMF induced in the loop is proportional to:
1.
\((\cos \alpha+\sin \alpha) \dfrac{d B}{d t}\)
2.
\( (\cos \alpha-\sin \alpha) \dfrac{d B}{d t}\)
3.
\((\tan \alpha+\cot \alpha) \dfrac{d B}{d t}\)
4.
\( (\tan \alpha-\cot \alpha) \dfrac{dB}{d t}\)
Subtopic: Faraday's Law & Lenz Law |
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A circular loop of radius \(R\), enters a region of uniform magnetic field \(B\) as shown in the diagram. The field \((B)\) is perpendicular to the plane of the loop while the velocity of the loop, \(v\), is along its plane. The induced EMF:
| 1. | increases continuously. |
| 2. | decreases continuously. |
| 3. | first increases and then decreases. |
| 4. | remains constant throughout. |
Subtopic: Faraday's Law & Lenz Law |
70%
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The current through the inductor in the figure is initially zero. The initial rate of change of the current \(i\) through the inductor (i.e. \(\dfrac{di}{dt}\)) is:
| 1. | zero | 2. | \(-\dfrac{I_{0} R}{L}\) |
| 3. | \(\dfrac{I_{0} R}{L}\) | 4. | \(\dfrac{I_{0} R}{2L}\) |
Subtopic: LR circuit |
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A rectangular conducting wire-frame having dimensions of \(a × 2a\) is bent symmetrically so that its two halves are at right-angle with respect to each other. A uniform, constant magnetic field \(B\) acts parallel to one of the bent sides, initially. The wire frame begins to rotate with a uniform angular speed \(\omega\) about the bend-line, \(PQ\). The emf induced in the loop will have the form:
| 1. | \(2\omega Ba^2\sin\omega t\) |
| 2. | \(2\omega Ba^2\cos\omega t\) |
| 3. | \(\omega Ba^2(\cos\omega t+\sin\omega t)\) |
| 4. | \(\omega Ba^2(\cos\omega t-\sin\omega t)\) |
Subtopic: Faraday's Law & Lenz Law |
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A triangular wire frame, in the form of an equilateral triangle \(PQR\) moves with a uniform velocity into a region where there is a uniform magnetic field \(B\). The edge \(PQ\) is parallel to the boundary of the region and the velocity \(v\) is perpendicular to it. The emf(\(E\)) induced within the frame is plotted as a function of time \(t,\) starting from when the frame enters the magnetic field. \(E\) is given by:
| 1. | \(Bv^2t\) | 2. | \(2Bv^2t\) |
| 3. | \(\dfrac{\sqrt3}{2}Bv^2t\) | 4. | \(\dfrac{2}{\sqrt3}Bv^2t\) |
Subtopic: Motional emf |
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A wire, bent into the shape of a right angled triangle \(PQR,\) lies with its side \(PR\) parallel to a current carrying wire, and side \(QR\) perpendicular to it. The loop lies in the plane of the wire. EMF induced in the loop when it is moved with constant speed along \(PR\) is \(\varepsilon_1\) and it is \(\varepsilon_2\) when moved along \(QR\) with the same constant speed. Then,
1. \(\varepsilon_1=0,\varepsilon_2\neq0\)
2. \(\varepsilon_1\neq0,\varepsilon_2=0\)
3. \(\varepsilon_1=0,\varepsilon_2=0\)
4. \(\varepsilon_1\neq0,\varepsilon_2\neq0\)
1. \(\varepsilon_1=0,\varepsilon_2\neq0\)
2. \(\varepsilon_1\neq0,\varepsilon_2=0\)
3. \(\varepsilon_1=0,\varepsilon_2=0\)
4. \(\varepsilon_1\neq0,\varepsilon_2\neq0\)
Subtopic: Motional emf |
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In the circuit shown in the adjoining figure, the switch was kept at the position \('1'\) for a long time. The switch \(K\) is suddenly (and smoothly) shifted to position \('2'.\)
The current through the cell, just after the shift, is:
The current through the cell, just after the shift, is:
| 1. | \(\dfrac{V_0}{2R}\) | 2. | \(\dfrac{V_0}{R}\) |
| 3. | \(\dfrac{3V_0}{4R}\) | 4. | zero |
Subtopic: LR circuit |
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A straight horizontal wire of mass \(m\) and length \(l,\) and having a negligible resistance can slide freely on a pair of conducting parallel rails, placed vertically. The rails are connected at the top by a capacitor \(C.\) A uniform magnetic field \(B\) exists in the region, perpendicular to the plane of the rails. The wire:
| 1. | falls with uniform velocity. |
| 2. | accelerates down with acceleration less than \(g\). |
| 3. | accelerates down with acceleration equal to \(g\). |
| 4. | moves down and eventually comes to rest. |
Subtopic: Motional emf |
71%
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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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