State the working of an a.c. generator with the help of a labelled diagram. The coil of an a.c. generator having N turns, each of area A, is rotated with a constant angular velocity ω. Deduce the expression for the alternating e.m.f. generated in the coil. What is the source of energy generation in this device?
Answer:e=NBAωsinωt; the energy comes from the mechanical work done in rotating the coil.
Solution
Working: A coil of N turns, each of area A, is rotated at constant angular speed ω in a uniform field B. The changing flux linkage induces an alternating emf, tapped through slip rings and brushes. Derivation: At time t the coil normal makes angle θ=ωt with B, so
ϕ=NBAcosωt
e=−dtdϕ=−dtd(NBAcosωt)=NBAωsinωt
The emf is maximum when sinωt=1, giving e0=NBAω, so
e=e0sinωt
Source of energy: the device does not create energy; the mechanical work done by the agency rotating the coil (against the opposing torque on the induced current) is converted into electrical energy.
