Question

A variable reluctance tachogenerator consists of a ferromagnetic gear wheel with 15 teeth rotating close to a magnet and coil assembly. The total flux N linked by the coil is given by

$N\left(\theta \right)=10+4\cos 150milliwebers$

where $\theta$ is the angular position of the wheel relative to the axis of the magnet. If the angular velocity of the wheel is 6000 r.p.m, then the frequency of the output signal is _________ kHz.

• A. 3
• B. 1.5
• C. 0.5
• D. 1

Answer 1

The correct option is B 1.5

For variable reluctance techogenerator

$N\left(\theta \right)=a+b\cos m\theta$

where, a = mean flux

b = amplitude of flux variation

m = number of teeth

Output signal of tachogenerator is given by

$E=\frac{dN}{d\theta }=bm{\omega }_r\sin m{\omega }_{r}t$ $[\because \theta ={\omega }_{r}t;\frac{d\theta }{dt}={\omega }_r]$

$\text{where,}{\omega }_r=\text{angular velocity of wheel}$

$Frequency,f=\frac{m{\omega }_r}{2\pi }=\frac{15\times 2\times 3.14\times 6000}{2\times 3.14\times 60}=1.5kHz$