Question 3.11: An iron-cored toroidal coil has 100 turns. The mean length o...
An iron-cored toroidal coil has 100 turns. The mean length of the flux path is 0.5 m an the cross-sectional area of the core is 10 cm². Calculate the inductance of the coil. Assume relative permeability of iron as 2000. Also calculate the induced emf in the coil when current of 5 A is reversed in 10 ms.
The expression for inductance in terms of its parameters is
L=\frac{\mu N^{2} A}{\ell }
where, \mu=\mu_{o} \mu_{r}
Current in the coil is changed from +5 A to −5 A in 10 × 10^{−3} secs. Total change of current is 10 A.
Putting the given values we get,
L=\frac{4π × 10^{−7} × 2000 × 100 × 100 × 10}{10000 × 0.5}
=\frac{4π × 10^{−4} × 2 × 10}{0.5}
= 16 × 3.14 × 10^{−3} H
= 50.24 × 10^{−3} H
= 50.24 mH
Induced EMF, e = −L \frac{di}{dt}
Average value of induced EMF, E = L \frac{change in current}{time taken}
E = L \frac{2I}{t}
Substituting values, E = 50.24 × 10^{−3} \frac{2 × 5}{10 × 10^{−3}}
= 50.24 V