Answer to Question #95511 in Electricity and Magnetism for NILAKSHA GHOSH

Question #95511
the initial angular speed of the coil in the generator is 5 rad/s and the initial amplitude of the induced emf is 10 v.calculate the angular speed of the coil in the generator when the amplitude of the induced emf is 8v
1
Expert's answer
2019-09-30T10:16:32-0400

The emf induced in the coil of electrical generator is given by formula


E=NABωsinωt{\mathcal E}=NAB\omega\sin\omega t

The amplitude of emf

Em=NABω{\mathcal E_m}=NAB\omega

Therefore


Em2Em1=ω2ω1\frac{\mathcal E_{m2}}{{\mathcal E_{m1}}}=\frac{\omega_2}{\omega_1}

Finally

ω2=Em2Em1ω1{\omega_2}=\frac{\mathcal E_{m2}}{{\mathcal E_{m1}}}{\omega_1}

ω2=8V10V×5rad/s=4rad/s{\omega_2}=\frac{8\:\rm V}{10\:\rm V}\times{5\:\rm rad/s}=4\:\rm rad/s


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