Question

If T is the time period of the rotation of the coil, at what values of T in a cycle, the emf generator is maximum ?

Answer 1

The induced emf in an a.c. generator is given by \[ e=E_0\sin(\omega t) \] where \(E_0\) is the maximum (peak) emf.

The emf is maximum when \[ \sin(\omega t)=\pm1 \] i.e., \[ \omega t=\frac{\pi}{2},\ \frac{3\pi}{2} \]

Since \[ \omega=\frac{2\pi}{T}, \] we get \[ t=\frac{\pi/2}{2\pi/T}=\frac{T}{4} \] and \[ t=\frac{3\pi/2}{2\pi/T}=\frac{3T}{4}. \]

Hence, in one complete cycle, the emf is maximum (positive and negative peak) at \[ \boxed{t=\frac{T}{4}\ \text{and}\ t=\frac{3T}{4}.} \]

• At \(t=\dfrac{T}{4}\): \(e=+E_0\) (maximum positive emf).
• At \(t=\dfrac{3T}{4}\): \(e=-E_0\) (maximum negative emf).