Question 3.12: There is mutual magnetic coupling between two coils of numbe...
There is mutual magnetic coupling between two coils of number of turns 500 and 2000, respectively. Only 50% of the flux produced by the coil of 500 turns is linked with the coil of 1000 turns. Calculate the mutual inductance of the two coils. Also calculate the EMF induced in the coil of 1000 turns when current changes at the rate of 10 A/second in the other coil. The self inductance of the coil of 500 turns in 200 mH.
Mutual inductance,
M=\frac{flux linkage in coil 2}{current change in coil 1}
= N_{2} \frac{KΦ_{1}}{I_{1}}= 2000 × \frac{0.5 × Φ_{1}}{I_{1}} = \frac{1000 Φ_{1}}{I_{1}}
L_{1} = \frac{N_{1} Φ_{1}}{I_{1}}
or, \frac{ Φ_{1}}{I_{1}} = \frac{ L_{1}}{N_{1}} = \frac{200 × 10^{-3}}{500}
M= 1000 × \frac{Φ_{1}}{N_{1}}= \frac{1000 × 200 × 10^{-3}}{500}
or, M = 400 × 10^{−3} H
Induced EMF in the second coil, e_{2} is
e_{2}= M \frac{di}{dt}
= 400 × 10^{−3} × 10
= 4 V
