Marks: 03 1. Name the parts of the electromagnetic spectrum which is (a) suitable for radar systems used in aircraft navigation. (b) used to treat muscular strain. (c) used as a diagnostic tool in medicine. Write in brief, how these waves can be produced.

Answer: (a) Microwave Production: Klystron/magnetron/Gunn diode (any one) (b) Infrared Radiation Production: Hot bodies / vibrations of atoms and molecules (any one) (c) X-Rays Production: Bombarding high energy electrons on metal target/ x-ray tube/inner shell electrons (any one).

Marks: 03

2. An inductor L of inductance XL is connected in series with a bulb B and an ac source. How would brightness of the bulb change when (i) number of turns in the inductor is reduced, (ii) an iron rod is inserted

in the inductor and (iii) a capacitor of reactance XC = XL is inserted in series in the circuit. Justify your answer in each case. Answer: (i) Increases

XL = ωL As number of turns decreases, L decreases, hence current through bulb increases. / voltage across bulb increases. (ii) Decreases

Iron rod increases the inductance, which increases XL, hence current through the bulb decreases / voltage across bulb decreases. (iii) Increases

Under this condition (XC = XL) the current through the bulb will become maximum / increase.

Marks: 05 3. (a) Define mutual inductance and write its S.I. unit. (b) Derive an expression for the mutual inductance of two long co- axial solenoids of same length wound one over the other.

(c) In an experiment, two coils c1 and c2 are placed close to each

other. Find out the expression for the emf induced in the coil c1 due

to a change in the current through the coil c2. Answer:

(a) Line integral of magnetic field over a closed loop is equal to the μ0 times the total current passing through the surface enclosed by the loop. Alternatively

Let the current flowing through each turn of the toroid be I. The total number of turns equals n.(2πr) where n is the number of turns per unit length. Applying Ampere's circuital law, for the Amperian loop, for interior points.

(b)

The solenoid contains N loops, each carrying a current I. Therefore, each loop acts as a magnetic dipole. The magnetic moment for a current I, flowing in loop of area (vector) A is given by m = IA The magnetic moments of all loops are aligned along the same direction. Hence, net magnetic moment equals NIA. OR (a) ϕ = MI Mutual inductance of two coils is equal to the magnetic flux linked with one coil when a unit current is passed in the other coil. Alternatively,

Mutual inductance is equal to the induced emf set up in one coil when the rate of change of current flowing through the other coil is unity. SI unit: henry / (weber ampere–1) / (volt second ampere–1) (Any one) (b)

Marks: 3 4. (i) Define mutual inductance. (ii) A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil ? Ans.

Marks: 3

5. Write Maxwell’s generalization of Ampere’s Circuital Law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is d i= E 0 dt

where ΦE is the electric flux produced during charging of the capacitor plates.

Ans.

Marks: 5

6. An a.c. source of voltage V = V0 sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit XL = R and power factor of the circuit is P1.

When capacitor with capacitance C such that XL = XC is put in series,

the power factor becomes P2. Calculate P1/P2. OR (i) Write the function of a transformer. State its principle of working with the help of a diagram. Mention various energy losses in this device. (ii) The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W. Calculate (a) number of turns in secondary (b) current in primary (c) voltage across secondary (d) current in secondary (e) power in secondary Ans.

Marks: 2 7. Identify the electromagnetic waves whose wavelengths vary as (a) 10–12 m < λ < 10–8 m (b) 10–3 m < λ < 10–1 m Write one use for each. Ans.

Marks: 3 8. Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other. OR Define self-inductance of a coil. Obtain the expression for the energy stored in an inductor L connected across a source of emf. Ans.

OR

Marks: 5

9. A device ‘X’ is connected to an ac source V = V0 sin ωt. The variation of voltage, current and power in one cycle is shown in the following graph:

(a) Identify the device ‘X’. (b) Which of the curves A, B and C represent the voltage, current and the power consumed in the circuit ? Justify your answer. (c) How does its impedance vary with frequency of the ac source ? Show graphically. (d) Obtain an expression for the current in the circuit and its phase relation with ac voltage. OR (a) Draw a labelled diagram of an ac generator. Obtain the expression for the emf induced in the rotating coil of N turns each of cross- sectional area A, in the presence of a magnetic field B. (b) A horizontal conducting rod 10 m long extending from east to west is falling with a speed 5·0 ms–1 at right angles to the horizontal component of the Earth’s magnetic field, 0·3 × 10–4 Wb m–2. Find the instantaneous value of the emf induced in the rod. Ans.

OR (a)