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So, suppose a dc shunt motor is running at full load. I wanted to know what happens to the torque, speed, armature current and line current when the load changes? How are these related mathematically. In my book it is given that " when load becomes half of the full load, line current also becomes half ", but why? What I think is that when we increase the load from no load to full load, torque increases and since torque is proportional to armature current for a dc shunt motor, armature current should also increase. But when we already are working at full load, maximum armature current would be flowing. So when load becomes half, shouldn't the armature current also become half?

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    \$\begingroup\$ "when load becomes half of the full load, line current also becomes half " and " So when load becomes half, shouldn't the armature current also become half" are the same statement. \$\endgroup\$ – Tom Carpenter Apr 15 '18 at 9:51
  • \$\begingroup\$ Line current is equal to armature current plus field current. Line current is not equal to armature current \$\endgroup\$ – Rishabhg Apr 15 '18 at 10:00
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    \$\begingroup\$ Generally the field winding carries a much smaller current (in a shunt-wound motor) than the armature, while developing the same voltage. So the statement that total current halves may be approximately correct even if it isn't strictly so. This is in definite contrast to a series-wound motor, where the field winding carries the same current as the armature but a smaller share of the voltage. \$\endgroup\$ – Chromatix Apr 15 '18 at 10:20
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In a dc shunt motor, the field resistance is generally very high. This is to avoid high current through field. On the other hand, we require high current through armature. Practically, you will find field resistance values in 100s of Ohms while armature resistance will be less than 1 Ohm or so. So, due to high field resistance, current through field will be very low compared to armature current.

So, as line current = armature current + field current, and field current is negligible compared to armature current, we can approximate line current to armature current.

Yes, torque is proportional to armature current in a dc shunt motor. So, when load increases, armature current increases and we can say that line current also increases by almost same amount because (again) field current is negligible compared to armature current.

Also note that, generally in Electrical Engineering, we refer to load as load current and not the impedance or other properties of actual load.

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