AC Generator - Principle and Working - UNSOLVED PRACTICE SET

Q7. Explain the principle of an AC generator with a diagram. What is the role of the armature, field magnets, slip rings, and brushes?

Q8. Derive the expression for the instantaneous EMF generated in a rotating coil in a uniform magnetic field.

Q9. A coil of 100 turns, area 0.1 m², rotates at 50 Hz in a magnetic field of 0.5 T. Calculate the maximum EMF generated.

Q10. Why does a DC generator use a commutator while an AC generator uses slip rings? Explain the difference.

Q11. The armature of an AC generator has 200 turns and area 0.05 m². It rotates at 1500 rpm in a field of 0.4 T. Calculate the peak voltage and the RMS voltage.

Q12. Why is the EMF zero when the plane of the coil is perpendicular to the magnetic field in an AC generator? Explain.

Q13. Explain the construction and working of an AC generator with a neat diagram. Derive the expression for the instantaneous EMF: ε = NABω sin ωt. Explain why the EMF is sinusoidal.

Q14. Explain the difference between an AC generator and a DC generator. How does a DC generator convert AC to DC using a commutator? Draw diagrams showing the output waveforms of both.

Q15. A rectangular coil of 200 turns, dimensions 20 cm × 30 cm, rotates at 3000 rpm in a uniform magnetic field of 0.6 T about an axis perpendicular to the field.

(a) Calculate the maximum EMF generated.

(b) Calculate the instantaneous EMF at t = 1/400 s.

(c) Calculate the average EMF over one complete cycle.

(d) If the coil resistance is 10 Ω and it is connected to an external resistance of 40 Ω, calculate the maximum current and the power delivered.

Q16. In a school science project, a student builds a small AC generator using a bicycle wheel. The armature consists of a coil with N = 100 turns, area A = 50 cm², mounted on the wheel axle. The student pedals at 60 rpm. A pair of permanent magnets provides a field B = 0.3 T.

(a) Calculate the frequency of the generated AC.

(b) Calculate the maximum EMF generated.

(c) Write the equation for instantaneous EMF as a function of time.

(d) The student connects a bulb rated 2.5 V, 0.5 A. Will the bulb glow? If not, suggest how to modify the generator.

(e) Calculate the mechanical power the student must supply to maintain the rotation, assuming 80% efficiency.

Q17. A hydroelectric power plant uses a generator with the following specifications: N = 20 pole pairs, armature with 120 turns per pole pair, area per turn = 2 m², magnetic field B = 0.8 T. The turbine rotates at 300 rpm.

(a) Calculate the frequency of the generated AC.

(b) Calculate the maximum EMF per phase.

(c) For a three-phase generator, calculate the line voltage if the phases are star-connected.

(d) The plant generates 100 MW. Calculate the torque exerted on the turbine (assuming 95% efficiency).

(e) Explain why power plants generate AC at high voltage (11 kV–33 kV) and use transformers to step up for transmission.

Q18. A single-phase AC generator has a rectangular coil with N = 500 turns, dimensions 40 cm × 60 cm, rotating at 1500 rpm in a uniform magnetic field B = 0.5 T. The coil resistance is 2 Ω.

(a) Calculate the maximum EMF, RMS EMF, and average EMF over half a cycle.

(b) The generator is connected to a load consisting of a 20 Ω resistor in series with a 0.1 H inductor. Calculate the impedance of the load at 50 Hz.

(c) Calculate the RMS current and the phase angle between voltage and current.

(d) Calculate the power delivered to the load and the power factor.

(e) Draw phasor diagrams showing the voltage, current, and voltage across each component.

(f) A student suggests adding a capacitor to improve the power factor. Calculate the capacitance needed for unity power factor.