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

Question

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

Answer 1

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

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

The amplitude of emf

$${\mathcal E_m}=NAB\omega$$

Therefore

$$\frac{\mathcal E_{m2}}{{\mathcal E_{m1}}}=\frac{\omega_2}{\omega_1}$$

Finally

$${\omega_2}=\frac{\mathcal E_{m2}}{{\mathcal E_{m1}}}{\omega_1}$$

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