A circular loop of area 5 x 10^–2 m² rotates in a uniform magnetic field of 0.2T. If the loop rotates about its diameter which is perpendicular to the magnetic field as shown in figure. Find the magnetic flux linked with the loop when its plane is
(i) normal to the field
(ii) inclined 60^o to the field and
(iii) parallel to the field.

A conducting rod of length 0.5 m falls freely from the top of a building of height 7.2 m at a place in Chennai where the horizontal component of Earth’s magnetic field is 4.04 × 10^–5 T. If the length of the rod is perpendicular to Earth’s horizontal magnetic field, find the emf induced across the conductor when the rod is about to touch the ground. (Assume that the rod falls down with constant acceleration of 10 m s^–2)

A solenoid of 500 turns is wound on an iron core of relative permeability 800. The length and radius of the solenoid are 40 cm and 3 cm respectively. Calculate the average emf induced in the solenoid if the current in it changes from 0 to 3 A in 0.4 second.

Consider two coplanar, co-axial circular coils A and B as shown in figure. The radius of coil A is 20 cm while that of coil B is 2 cm. The number of turns in coils A and B are 200 and 1000 respectively. Calculate the mutual inductance between the coils. If the current in coil A changes from 2 A to 6 A in 0.04 s, determine the induced emf in coil B and the rate of change of flux through the coil B at that instant.

A circular metal of area 0.03 m² rotates in a uniform magnetic field of 0.4 T. The axis of rotation passes through the centre and perpendicular to its plane and is also parallel to the field. If the disc completes 20 revolutions in one second and the resistance of the disc is 4 Ω, calculate the induced emf between the axis and the rim and induced current flowing in the disc.

A rectangular coil of area 70 cm² having 600 turns rotates about an axis perpendicular to a magnetic field of 0.4 Wb m^–2. If the coil completes 500 revolutions in a minute, calculate the instantaneous emf when the plane of the coil is
(i) perpendicular to the field
(ii) parallel to the field and
(iii) inclined at 60^o with the field.

An ideal transformer has 460 and 40,000 turns in the primary and secondary coils respectively. Find the voltage developed per turn of the secondary if the transformer is connected to a 230 V AC mains. The secondary is given to a load of resistance 10⁴ Ω. Calculate the power delivered to the load.

An inverter is common electrical device which we use in our homes. When there is no power in our house, inverter gives AC power to run a few electronic appliances like fan or light. An inverter has inbuilt step-up transformer which converts 12 V AC to 240 V AC. The primary coil has 100 turns and the inverter delivers 50 mA to the external circuit. Find the number of turns in the secondary and the primary current.

Write down the equation for a sinusoidal voltage of 50 Hz and its peak value is 20 V. Draw the corresponding voltage versus time graph.

A capacitor of capacitance \(\frac { { 10 }^{ -4 } }{ \pi } F\), an inductor of inductance \(\frac { 2 }{ \pi } H\) and a resistor of resistance 100 Ω are connected to form a series RLC circuit. When an AC supply of 220 V, 50 Hz is applied to the circuit, determine
(i) the impedance of the circuit
(ii) the peak value of current flowing in the circuit
(iii) the power factor of the circuit and
(iv) the power factor of the circuit at resonance.

The equation for an alternating current is given by i = 77 sin 314t. Find the peak current, frequency, time period and instantaneous value of current at t = 2 ms.

Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively.

A series RLC circuit which resonates at 400 kHz has 80 μH inductors, 2000 pF capacitor and 50 Ω resistor. Calculate
(i) Q-factor of the circuit
(ii) the new value of capacitance when the value of inductance is doubled and
(iii) the new Q-factor.

The current in an inductive circuit is given by 0.3 sin (200t – 40°) A. Write the equation for the voltage across it if the inductance is 40 mH.

A 500 μH inductor, \(\\ \frac { 80 }{ { \pi }^{ 2 } } pF\) capacitor and a 628 Ω resistor are connected to form a series RLC circuit. Calculate the resonant frequency and Q-factor of this circuit at resonance.

Find the instantaneous value of alternating voltage v = 10sin (3π x 10⁴ t) volt at
i) 0 s
ii) 50 μs
iii) 75 μs.

What are step-up and step-down transformers?

Obtain an expression for motional emf from Lorentz force.

A 50 cm long solenoid has 400 turns per cm. The diameter of the solenoid is 0.04 m. Find the magnetic flux linked with each turn when it carries a current of 1 A.

A coil of 200 turns carries a current of 0.4 A. If the magnetic flux of 4 mWb is linked with each turn of the coil, find the inductance of the coil.

Two air core solenoids have the same length of 80 cm and same cross-sectional area 5 cm². Find the mutual inductance between them if the number of turns in the first coil is 1200 turns and that in the second coil is 400 turns.

A long solenoid having 400 turns per cm carries a current 2A. A 100 turn coil of cross-sectional area 4 cm² is placed co-axially inside the solenoid so that the coil is in the field produced by the solenoid. Find the emf induced in the coil if the current through the solenoid reverses its direction in 0.04 sec.

A 200 turn circular coil of radius 2 cm is placed co-axially within a long solenoid of 3 cm radius. If the turn density of the solenoid is 90 turns per cm, then calculate mutual inductance of the coil and the solenoid.

The solenoids S₁ and S₂ are wound on an iron-core of relative permeability 900. The areas of their cross-section and their length are the same and are 4 cm² and 0.04 m respectively. If the number of turns in S₁ is 200 and that in S₂ is 800. Calculate the mutual inductance between the solenoids. If the current in solenoid 1 is increased form 2A to 8A in 0.04 second. Calculate the induced emf in solenoid 2.

A step-down transformer connected to main supply of 220 V is used to operate 11V, 88W lamp. Calculate
(i) Voltage transformation ratio and
(ii) Current in the primary.

A 200V/120V step-down transformer of 90% efficiency is connected to an induction stove of resistance 40 Ω. Find the current drawn by the primary of the transformer.

The 300 turn primary of a transformer has resistance 0.82 Ω and the resistance of its secondary of 1200 turns is 6.2 Ω. Find the voltage across the primary if the power output from the secondary at 1600V is 32 kW. Calculate the power losses in both coils when the transformer efficiency is 80%.