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JEE Mains | PYQ

Two coils have mutual inductance \( 0.002 \, \text{H} \). The current changes in the first coil according to the relation \( i = i_0 \sin \omega t \), where \( i_0 = 5 \, \text{A} \) and \( \omega = 50 \pi \, \text{rad/s} \). The maximum value of emf in the second coil is \( \frac{\pi}{\alpha} \, \text{V} \). The value of \( \alpha \) is __________.

When a coil is connected across a \( 20 \, \text{V} \) dc supply, it draws a current of \( 5 \, \text{A} \). When it is connected across \( 20 \, \text{V}, 50 \, \text{Hz} \) ac supply, it draws a current of \( 4 \, \text{A} \). The self inductance of the coil is ________ \( \text{mH} \). (Take \( \pi = 3 \) )

Two conducting circular loops \( A \) and \( B \) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:

A square loop \( PQRS \) having \( 10 \) turns, area \( 3.6 \times 10^{-3} \, \text{m}^{2} \) and resistance \( 100 \, \Omega \) is slowly and uniformly being pulled out of a uniform magnetic field of magnitude \( B = 0.5 \, \text{T} \) as shown. Work done in pulling the loop out of the field in \( 1.0 \, \text{s} \) is ______ \( \times 10^{-6} \, \text{J} \).

A square loop of side \( 10 \, \text{cm} \) and resistance \( 0.7 \, \Omega \) is placed vertically in east-west plane. A uniform magnetic field of \( 0.20 \, \text{T} \) is set up across the plane in north east direction. The magnetic field is decreased to zero in \( 1 \, \text{s} \) at a steady rate. Then, magnitude of induced emf is \( \sqrt{x} \times 10^{-3} \, \text{V} \). The value of \( x \) is __________.

A rod of length \( 60 \, \text{cm} \) rotates with a uniform angular velocity \( 20 \, \text{rad s}^{-1} \) about its perpendicular bisector, in a uniform magnetic field \( 0.5 \, \text{T} \). The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _______________ \( \text{V} \).

The magnetic flux \( \phi \) (in weber) linked with a closed circuit of resistance \( 8 \, \Omega \) varies with time (in seconds) as \( \phi = 5t^2 - 36t + 1 \). The induced current in the circuit at \( t = 2 \, \text{s} \) is __________ A.

Given below are two statements:
Statement (I): When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account.
Statement (II): Ampere's circuital law does not depend on Biot-Savart's law.
In the light of the above statements, choose the correct answer from the options given below:

The current in an inductor is given by \( I = (3t + 8) \) where \( t \) is in second. The magnitude of induced emf produced in the inductor is \( 12 \, \text{mV} \). The self-inductance of the inductor _____ \( \text{mH} \).

A transformer has an efficiency of \( 80\% \) and works at \( 10\,\text{V} \) and \( 4\,\text{kW} \). If the secondary voltage is \( 240\,\text{V} \), then the current in the secondary coil is:

A coil is placed perpendicular to a magnetic field of \( 5000 \, \text{T} \). When the field is changed to \( 3000 \, \text{T} \) in \( 2 \, \text{s} \), an induced emf of \( 22 \, \text{V} \) is produced in the coil. If the diameter of the coil is \( 0.02 \, \text{m} \), then the number of turns is the coil is:

A horizontal straight wire \( 5 \, \text{m} \) long extending from east to west falling freely at right angle to horizontal component of earths magnetic field \( 0.60 \times 10^{-4} \, \text{wB m}^{-2} \). The instantaneous value of emf induced in the wire when its velocity is \( 10 \, \text{m s}^{-1} \) is __________ \( \times 10^{-3} \, \text{V} \).

In a coil, the current changes from \( -2 \, \text{A} \) to \( +2 \, \text{A} \) in \( 0.2 \, \text{s} \) and induces an emf of \( 0.1 \, \text{V} \). The self inductance of the coil is:

A square loop of side \(15 \, \text{cm}\) being moved towards right at a constant speed of \(2 \, \text{cm/s}\) as shown in figure. The front edge enters the \(50 \, \text{cm}\) wide magnetic field at \(t = 0\). The value of induced emf in the loop at \(t = 10 \, \text{s}\) will be:

A rectangular loop of length \( 2.5 \, \text{m} \) and width \( 2 \, \text{m} \) is placed at \( 60^\circ \) to a magnetic field of \( 4 \, \text{T} \). The loop is removed from the field in \( 10 \, \text{s} \). The average emf induced in the loop during this time is :