Question 7.18: Three coils are wound on a cast steel core as shown in Fig. ...
Three coils are wound on a cast steel core as shown in Fig. 7.33. The current directions in coils are indicated in the figure core data.
Cross-sectional area, A_{c} = 12 cm²
Mean path length, I_{c} = 30 cm
Coils data
A 200 turns, 1A
B 600 turns, 0.75 A
C ? 0.5 A
How many turns should coil C have create core flux of 1.5 mWb.
Core flux = 1.5 mWb
Core cross-section = 12 cm²
Core flux density, B_{c} = \frac{1.5 × 10^{-3} }{12 × 10^{-4}} = 1.25 T
From the magnetization curve of cast steel of Fig. 7.33 corresponding to B_{c} = 1.25 T
H_{C} = 1250 AT/m
Total mmf needed F = H_{C} l_{C} = 1250 × 0.30 = 375 AT
AT_{a} = 200 × 1 = 200
AT_{b} = 600 × 0.75 = 450
As per right hand rule AT_{a} and AT_{b} oppose each other. So
AT_{b} – AT_{a} = 450 – 200 = 250 (downwards)
AT_{c} aids AT_{b} , so
F = AT_{b} – AT_{a} + AT_{c} = 375
or AT_{c} = 375 – 250 = 125
Number of turns of coil C
N_{C} = \frac{125}{0.5} = 250
Direction of flux is clockwise.