\(AB\) is a part of an electrical circuit (see figure). The potential difference \(''V_{A}-V_{B}'',\) at the instant when current \(i=2~\text A\) and is increasing at a rate of \(1~\text{amp/second}\) is:
            
1. \(9~ \text{volts}\)
2. \(10~ \text{volts}\)
3. \(5~ \text{volts}\)
4. \(6~ \text{volts}\)
Subtopic:  LR circuit |
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In the above diagram, a strong bar magnet is moving towards solenoid-\(2\) from solenoid-\(1\). The direction of induced current in solenoid-\(1\) and that in solenoid-\(2\), respectively, are through the directions:
1. \(BA\) and \(CD\) 2. \(AB\) and \(CD\)
3. \(BA\) and \(DC\) 4. \(AB\) and \(DC\)
Subtopic:  Faraday's Law & Lenz Law |
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A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to:
\(\mathrm A.\) hold the sheet there if it is magnetic.
\(\mathrm B.\) hold the sheet there if it is non-magnetic.
\(\mathrm C.\) move the sheet away from the pole with uniform velocity if it is conducting.
\(\mathrm D.\) move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar.
Choose the correct statement\((\mathrm s )\) from the options given below:
1. \(\mathrm A\) and \(\mathrm C\) only
2. \(\mathrm A\), \(\mathrm C\) and \(\mathrm D\) only
3. \(\mathrm C\) only
4. \(\mathrm B\) and \(\mathrm D\) only
Subtopic:  Faraday's Law & Lenz Law |
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An ideal inductor-resistor-battery circuit is switched on at \(t=0~\text{s}\). At time \(t\), the current is \(i=i_0\left(1-e^{\left(-\frac{t}{\tau}\right)}\right)\text{A}\), where \(i_0\) is the steady-state value. The time at which the current becomes \(0.5i_0\) is: [Given \(\text{ln}(2)= 0.693\)]
1. \(6.93 \times 10^3 ~\text{s}\)
2. \(6.93~\text{ms}\)
3. \(69.3~\text{s}\)
4. \(6.93~\text{s}\)
Subtopic:  LR circuit |
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A conducting circular loop of face area \(2.5 \times 10^{-3}~\text{m}^2\) is placed perpendicular to a magnetic field which varies as \(B=0.5~\text{sin}(100 \pi t)~\text{T}\). The magnitude of induced EMF at time \(t= 0~\text{s}\) is: 
1. \(0.125 \pi~ \text{mV}\)
2. \(125 \pi ~\text{mV}\)
3. \(125 \pi~\text{V}\)
4. \(12.5 \pi~\text{mV}\)
Subtopic:  Faraday's Law & Lenz Law |
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A rod of length \(L\) rotates with a small uniform angular velocity \(\omega\) about its perpendicular bisector. A uniform magnetic field \(B\) exists parallel to the axis of rotation. The potential difference between the centre of the rod and an end is:
1. \(\Large\frac{B\omega L^2}{8}\) 2. \(\Large\frac{B\omega L^2}{2}\)
3. \(\Large\frac{B\omega L^2}{4}\) 4. zero
Subtopic:  Motional emf |
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Let us consider two solenoids \(A\) and \(B,\) made from the same magnetic material of relative permeability \(\mu_{r}\) and of equal area of cross-section. Length of \(A\) is twice that of \(B\) and the number of turns per unit length in \(A\) is half that of \(B.\) The ratio of self-inductances of the two solenoids, \(L_A:L_B\) is:
1. \(1:2\)
2. \(2:1\)
3. \(8:1\)
4. \(1:8\)
Subtopic:  Self - Inductance |
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The magnetic energy stored in an inductor of inductance \(4~\mu\text{H}\) carrying a current of \(2~\text{A}\) is:
1. \(8~\mu \text{J}\)
2. \(4~\mu \text{J}\)
3. \(4~\text{mJ}\)
4. \(8~\text{mJ}\)
Subtopic:  Self - Inductance |
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An emf is generated by an ac generator having \(100\) turn coil, of loop area \(1\) m2. The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of \(0.05\) T perpendicular to the axis of rotation of the coil. The maximum value of emf is:
1. \(3.14\) V
2. \(31.4\) V
3. \(62.8\) V
4. \(6.28\) V
Subtopic:  Motional emf |
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A square loop with a side length of \(1~\text m\) and resistance of \(1~\Omega\) is placed in a uniform magnetic field of \(0.5~\text T.\) The plane of the loop is perpendicular to the direction of the magnetic field. The magnetic flux through the loop is:
1. zero
2. \(2\) Wb
3. \(0.5\) Wb
4. \(1\) Wb
Subtopic:  Magnetic Flux |
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