At time t = 0 , terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I t = I 0 cos ω t , with I 0 = 1 A and ω = 500 rad s - 1 starts flowing in it with the initial direction shown in the figure. At t = 7 π 6 ω , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 μ F , R = 10 Ω and the battery is ideal with of 50 V , identify the correct statement(s).

Magnitude of the maximum charge on the capacitor before t = 7 π 6 ω is 1 × 10 - 3 C .

The current in the left part of the circuit just before t = 7 π 6 ω is clockwise.

A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time t = 0 , the rod starts moving on the rails with a speed v = 3 . 0 m s - 1 (see the figure). A resistor R = 1.4 Ω and a capacitor C 0 = 5.0 μF are connected in series between the rails. At time t = 0 , C 0 is uncharged. Which of the following statement(s) is (are) correct? [ μ 0 = 4 π × 10 − 7 SI units. Take ln 2 = 0.7 ]

Maximum charge on capacitor C 0 is 8.4 × 10 − 12 coulomb.

Maximum current through R is 3.8 × 10 − 6 ampere.

Maximum charge on capacitor C 0 is 2 .4 × 10 − 12 coulomb.

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)

rotate in the same direction as the direction of magnet's motion.

rotate in the direction opposite to the direction of magnet's motion.

not rotate and its temperature will remain unchanged.

not rotate but its temperature will slowly rise.

In the circuit shown, initially there is no charge on capacitors and keys S 1 and S 2 are open. The values of the capacitors are C 1 = 10 μ F , C 2 = 30 μ F and C 3 = C 4 = 80 μ F . Which of the statement(s) is/are correct?

If key S 1 is kept closed for long time such that capacitors are fully charged, the voltage across the capacitors C 1 will be 4 V .

If key S 1 is kept closed for long time such that capacitors are fully charged, the voltage difference between points P and Q will be 10 V .

The keys S 1 is kept closed for long time such that capacitors are fully charged. Now key S 2 is closed, at this time, the instantaneous current across 30 Ω resistor (between points P and Q ) will be 0.2 A (round off to 1 s t decimal place).

A conducting wire of parabolic shape, initially y = x 2 , is moving with velocity V → = V 0 i ^ in a non-uniform magnetic field B → = B 0 1 + y L β k ^ , as shown in figure. If V 0 , B 0 , L and β are positive constants and Δ ϕ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are:

Δ ϕ remains the same if the parabolic wire is replaced by a straight wire, y = x initially, of length 2 L

Δ ϕ = 1 2 B 0 V 0 L for β = 0

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 17 - Electromagnetic Induction and Alternating Currents>JEE Advanced Paper 1 - 2017>Q 17

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

In the circuit shown, $L = 1 μ H, C = 1 μ F a n d R = 1 k Ω .$ They are connected in series with an a.c. source $V = V_{0} \sin ω t$ as shown. Which of the following options is/are correct?

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Important Questions on Electromagnetic Induction and Alternating Currents

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 17 - Electromagnetic Induction and Alternating Currents>JEE Advanced Paper 1 - 2017>Q 18

A circular insulated copper wire loop is twisted to form two loops of area

A

and

2 A

as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field

\vec{B}

points into the plane of the paper. At

t = 0

, the loop starts rotating about the common diameter as axis with a constant angular velocity in the magnetic field. Which of the following options is/are correct?
Question Image

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 17 - Electromagnetic Induction and Alternating Currents>JEE Advanced Paper 1 - 2016>Q 19

An infinite line charge of uniform electric charge density

λ

lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity

ε

and electrical conductivity

σ

. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 17 - Electromagnetic Induction and Alternating Currents>JEE Advanced Paper 1 - 2016>Q 20

A conducting loop in the shape of right angled isosceles triangle of height

10 cm

is kept such that the

90^{o}

vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at constant rate of