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Two coils of self inductance \( L_1 \) and \( L_2 \) are connected in series combination having mutual inductance of the coils as \( M \). The equivalent self inductance of the combination will be:

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)

Magnetic flux (in weber) in a closed circuit of resistance \( 20 \, \Omega \) varies with time \( t \, (\text{s}) \) as \( \phi = 8t^{2} - 9t + 5 \). The magnitude of the induced current at \( t = 0.25 \, \text{s} \) will be ________ \( \text{mA} \).

For the given circuit the current through battery of \( 6 \, \text{V} \) just after closing the switch ‘\( S \)’ will be _____ \( \text{A} \).

A coil of inductance \( 1 \, \text{H} \) and resistance \( 100\Omega \) is connected to a battery of \( 6 \, \text{V} \). Determine approximately:
(a) The time elapsed before the current acquires half of its steady–state value
(b) The energy stored in the magnetic field associated with the coil at an instant \( 15 \, \text{ms} \) after the circuit is switched on (Given \( \ln 2 = 0.693 \), \( e^{-3/2} = 0.25 \))

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

A \( 10 \, \Omega \), \( 20 \,\mathrm{mH} \) coil carrying constant current is connected to a battery of \( 20 \, \mathrm{V} \) through a switch. Now after switch is opened current becomes zero in \( 100 \, \mu \mathrm{s} \). The average e.m.f. induced in the coil is _____ \( \mathrm{V} \).

A circular coil of \( 1000 \) turns each with area \( 1 \, \text{m}^{2} \) is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of \( 0.07 \, \text{T} \). The maximum voltage generation will be ________ \( \text{V} \).

Match List I with List – II

Choose the CORRECT answer from the options given below:

Given below are two statements:
Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.
Statement II: In a material medium, the EM wave travels with speed \( v = \frac{1}{\sqrt{\mu_0 \, \varepsilon_0}} \). In the light of the above statements, choose the correct answer from the options given below.

A transformer operating at primary voltage \( 8 \, \text{kV} \) and secondary voltage \( 160 \, \text{V} \) serves a load of \( 80 \, \text{kW} \). Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be:

A metallic conductor of length \( 1 \, \text{m} \) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \( 5 \, \text{rad s}^{-1} \). If the horizontal component of earth's magnetic field is \( 0.2 \times 10^{-4} \, \text{T} \), then emf induced between the two ends of the conductor is:

In a coil of resistance \( 8 \, \Omega \), the magnetic flux to an external magnetic field varies with time as \( \phi = \dfrac{2}{3} \left( 9 - t^{2} \right) \). The value of total heat produced in the coil, till the flux becomes zero, will be __________ \( \text{J} \).

A conducting circular loop is placed in X–Y plane in presence of magnetic field \( \vec{B} = (3 t^3 \, \hat{j} + 3 t^2 \, \hat{k}) \) in SI unit. If the radius of the loop is \( 1 \, \text{m} \), the induced emf in the loop, at time \( t = 2 \, \text{s} \) is \( n\pi \, \text{V} \). The value of \( n \) is _____.

The magnetic flux through a coil perpendicular to its plane is varying according to the relation \( \phi = (5t^3 + 4t^2 + 2t - 5) \) Weber. If the resistance of the coil is \( 5 \, \text{ohm} \), then the induced current through the coil at \( t = 2 \, \text{s} \) will be:

The displacement current of \( 4.425 \, \mu\text{A} \) is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of \( 10^{6} \, \text{V s}^{-1} \). The area of each plate of the capacitor is \( 40 \, \text{cm}^{2} \). The distance between each plate of the capacitor is \( x \times 10^{-3} \, \text{m} \). The value of \( x \) is, (Permittivity of free space, \( E_{0} = 8.85 \times 10^{-12} \, \text{C}^{2}\text{N}^{-1}\text{m}^{-2} \)) ______.

A small square loop of wire of side \( l \) is placed inside a large square loop of wire \( L \) \( (L \gg l) \). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is:

The current in a coil of self inductance \( 2.0 \, \text{H} \) is increasing according to \( I = 2 \sin(t^2) \, \text{A} \). The amount of energy spent during the period when current changes from \( 0 \) to \( 2 \, \text{A} \) is __________ \( \text{J} \).

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JEE Main 2022 25th June Morning Shift

Match List I with List – II

Choose the CORRECT answer from the options given below: