Ac Generator

NCERT Class 12, Chapter 6 (Electromagnetic Induction) explains that an AC generator produces a sinusoidal emf as its coil rotates, with peak value ${\epsilon }_0=NBA\omega$, arising because the flux through the coil varies as $\cos \omega t$ and its rate of change is maximum when the coil plane is parallel to the field. Substituting: ${\epsilon }_0=100\times 0.4\times 0.05\times 60=120\text{V}$. The option 60 V halves the result by dropping a factor of two somewhere in the product. The option 240 V doubles it, perhaps by mis-reading the turns. The option 12 V drops a factor of ten in the area or turns. As a sanity check, the units combine as (turns × T × m² × rad/s), and since ${\text{Tcdotpm}}^2=\text{Wb}$ and $\text{Wb/s}=\text{V}$, the result is correctly in volts. A peak emf of 120 V is realistic for such a compact laboratory generator, and the actual output alternates sinusoidally between $+120$ V and $-120$ V. It is instructive to see that the peak emf depends linearly on the rotational speed, so spinning the coil twice as fast would double both the peak voltage and the output frequency. The emf is zero at the instant the coil plane is perpendicular to the field, because the flux is then maximum and momentarily unchanging, and it is greatest a quarter-turn later when the flux is changing most rapidly. This continuous conversion of mechanical rotational energy into electrical energy is the fundamental operating principle behind the generators that supply electrical power stations worldwide.