CHAPTER 16: ELECTROMAGNETIC INDUCTION
1. A conductor moves through a uniform magnetic field of flux density 25 mT at a velocity of 5 m/s. If the length of conductor within the field is 100 mm, calculate the voltage induced into the conductor, if it cuts the flux (a) perpendicularly, and (b) at 30°. [Answer: (a) 12.5 mV; (b) 6.25 mV]
2. An aeroplane, having a wingspan of 50 m is flying horizontally at a velocity of 600 km/h. Calculate the potential difference induced across the wingtips, assuming the vertical component of the earth’s magnetic field is 40 μT. [Answer: 0.33 V]
3. Calculate the inductance of a ring-shaped coil of mean diameter 200 mm, having 500 turns evenly wound around a wooden core of diameter 20 mm. If the wooden core is replaced by an iron core, having a relative permeability of 600 when the current is 5 A, what is the new value of inductance? [Answer: 157 μH ; 94.2 mH]
4. A non-magnetic ring, of mean diameter 300 mm and cross-sectional area 500mm2, is uniformly wound with a coil of 200 turns. What is the inductance of the coil? [Answer: 26.67 H]
5. A coil consists of 750 turns, and a current of 10 A results in a magnetic flux of 1200 μWb established within the coil. Calculate the inductance of the coil, and the average voltage induced into the coil, if the current is reversed in a period of 0.01 s. [Answer: 0.09 H; 180 V]
6. A coil of inductance 20 mH and resistance 2 Ω is suddenly connected to a 50-V d.c. supply. What will be (a) the maximum value that the current will eventually reach; (b) the time constant, (c) the current at a time equal to the time constant, and (d) the time taken for the current to reach its maximum value. [Answer: (a) 25 A; (b) 10 ms; (c) 15.8s; 50 ms]
7. How much energy will be stored in the magnetic field of a coil having a self-inductance of 16 mH and resistance 2 Ω, when connected to a 10-V d.c. supply? [Answer: 0.2 J]
8. Calculate the mutual inductance between two coils, of self inductance 2 mH and 25 μH, if their coefficient of coupling is 0.8. [Answer: 179 μH]
9. Two coils of self-inductance 8 mH and 16 mH have a mutual inductance of 8.48mH. What is their coefficient of coupling? [Answer: 0.75]
10. A transformer’s primary winding has 200 turns, and its secondary winding has 1000 turns. If the primary voltage is 100 V, what will be its secondary voltage? [Answer: 500 V]
11. If the above transformer supplies a load current of 2.5 A, what will be the value of its primary current? [Answer: 12.5 A]
12. An inductive circuit comprises two inductors that are installed in series on a circuit board in such a direction, and so close together, that they are cumulatively coupled. If the two inductors are 16 mH and 20mH, and the coefficient of coupling is 0.3, what will be total inductance of the circuit? [46.73 mH]
13. If one of the inductors, described above, was rewired so that it faced in the opposite direction, what would be the total inductance of the circuit? [Answer: 25.3H]