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Q1. Why a small resistor is usually put in parallel to the current carrying coil of an electromagnet?

Solution

When the current in the coil of a large electromagnet is switched off the magnetic flux changes at a very high rate. Thus the induced emf is very high and may cause sparking and can damage the insulation. A small resistor connected in parallel provides a conducting path to the induced emf and thus reduces the risk of sparking.

Q2. If a small plane circular coil with radius r with  number of turns is placed at a distance A from a straight vertical conductor in the same plane as of coil. What will be the mutual induction between the two?

• 1)
• 2)
• 3)
• 4)

Solution

Q3. How does the self-inductance of an air coil change, when (i) the number of turns in the coil is decreased (ii) an iron rod is introduced in the coil.

Solution

(i) Self inductance of a coil  N² When number of turns in coil is decreased, the self inductance will decrease. (ii) When an iron rod is introduced in the coil, the self-inductance of coil increases.

Q4. How does the mutual inductance of a pair of coils change when (i) the distance between the coils is increased and(ii) the number of turns in each coil is decreased ? Justify your answer in each case.

Solution

(i) When two coils move farther, the magnetic flux linked with the secondary coil decreases, so mutual inductance of coils decreases (ii) Mutual inductance M  N₁N₂, when number of turns in both coils decrease, the mutual inductance decreases.

Q5. Find the emf induced in the coil of 200 turns and cross-section area 0.4 m², when a magnetic field perpendicular to the plane of the coil changes from 0.1 Wbm^-2 to 0.5 Wbm^-2, at a uniform rate over a period of 0.04 sec.

Solution

Given: N = 200 A = 0.4m² B₁= 0.1 Wbm^-2 B₂= 0.5 Wbm^-2 t = 0.04 sec                    

Q6. Which rule helps in finding the current induced in an AC generator?

Solution

Fleming’s Right Hand rule helps in finding the current induced in an AC generator.

Q7. In the closed circuit of resistance(r) 10 Ω, the magnetic flux Φ  varies with time t according to the equation Φ = (6t² - 9t +3) milli weber. Calculate the magnitude of induced current at t = 0.5 second.

Solution

Q8. A copper rod of length 0.8 m rotates about one of its ends in a magnetic field of induction 0.6 Wb/m², the plane of the rotation being at right angle to the field. Find the change in the magnetic flux in a rod?

Solution

Given: l = 0.8m B = 0.6 Wb/m² θ = 0 Area (A) swept in one complete rotation = πl² Therefore change in magnetic flux = BA = B ×πl²                                                     = 0.6 × 3.14 × 0.8 × 0.8                                                     = 1.20576 Wb.

Q9. When the magnetic flux passing through a coil changes, will the induced emf and current be always produced in the coil ?

Solution

Due to change in magnetic flux the induced EMF will always be produced but current will be induced only if the circuit is closed.

Q10. a) What will be the direction of the induced current in the following setup? In figure b) a steady current flows through the wire find the direction of induced emf?

Solution

a) When the south pole of a magnet is being pushed towards the coil, the amount of magnetic flux linked with the coil increases. The current is induced in the coil in such a way that it opposes the increase in flux. It is possible only when current is induced in clockwise direction.   b) In the figure it is clear that, steady current flows through the wire. Therefore, no current is induced in the loop.

Q11. What are the observations made by Faraday in his experiment given below?

Solution

In the above experiment of Faraday, when the bar magnet is moved w.r.t the coil, following observations were made: i. Whenever there is a relative motion between the coil and the magnet, the galvanometer shows a sudden deflection. This deflection indicates the current is induced in the coil. ii. The deflection is temporary. It lasts so long as relative motion between the coil and the magnet continues. iii. The deflection is more when the magnet is moved faster and less when the magnet is moved slowly. iv. The direction of deflection is reversed when the same pole of the magnet is moved in the opposite direction or opposite pole of magnet is moved in the same direction.  

Q12. Calculate the mutual inductance of a 1 m long coil with 0.4 m radius and 1000 turns has a secondary of 500 turns wound near its mid-point.

Solution

Q13. Describe briefly, with the help of a labeled diagram, the basic elements of an A.C. generator. State its underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop.

Solution

Basic elements of an A.C. generator An A.C. generator consists of a rotor shaft on which a coil is mounted. A magnetic field is created around an armature coil with the help of permanent magnets.The terminals of the coil are connected to two slip rings. Carbon brushes are attached to slip rings so as to make connection with an external circuit.Underlying principle of an A.C. generatorThe underlying principle responsible for the working of an ?.C. generator is electromagnetic induction. According to this principle, if a conductor is placed in a varying magnetic field, then current is induced in the conductor.

Q14. In an a.c generator, coil of N turns and area A is rotated at V revolutions per second in a uniform magnetic field B.Write the expression for the emf produced. A 100-turn coil of area 0.1 m² rotates at half a revolution per second. It is placed in a magnetic field 0.01 T perpendicular to the axis of rotation of the coil. Calculate the maximum voltage generated in the coil.

Solution

Q15.  Calculate total inductance.

Solution

Q16. What are Foucault currents?

Solution

Foucault currents also called as Eddy currents are the induced currents when the magnetic flux linked with a conductor changes with time.  

Q17. When is the magnetic flux linked with the circuit (a) maximum and (b) minimum?

Solution

a) The magnetic flux is maximum when the plane of the coil is perpendicular to the magnetic field i.e, θ = 0° Therefore, Φ = NBA cos θ = NBA cos 0° =NBA (maximum). b) The magnetic flux is minimum when the plane of the coil is parallel to the magnetic field i.e θ = 90° Therefore, Φ = NBA cos θ = NBA cos 90° = 0 (minimum).

Q18. It is said that eddy currents have advantages and disadvantages too. What are the disadvantages?

Solution

Yes Eddy current has its own disadvantages. a)      Eddy currents oppose relative motion. b)      There is a lot of energy loss in form of heat. c)      Due o excessive heat loss, the appliance life gets reduced.

Q19. Why does the core is laminated in transformers?

Solution

The core in transformers is laminated to reduce the effect of eddy currents. The core is formed in form of thin sheets or laminas which are coated with an insulated materials and many such sheets are used together to form the laminated core of transformer. This increase the resistance between the sheets and confines the eddy currents to the individual sheets.

Q20. The figure shows the variation of field strength versus time of a loop kept in a magnetic field From the graph answer the following questions: a) Would there be any induced voltage if yes state when? b) During BC, CD and DE will there be flow of current?

Solution

a) Yes there will be induced voltage and it will be induced when the magnetic field changes with time i.e. in regions BC and CD. b) Yes there will be flow of current during BC and CD but there won't be flow of current during DE as the magnetic field is constant with time. Hence no induced voltage and no current.

Q21. On what factor does the frequency of an AC generator depend?

Solution

The frequency of an AC generator depends only on the speed of rotation of the coil.

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