What are the differences between them? Like why is the shunt feld different from the resistances of the armature and series field?
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These are related to DC machines.
They primarily differ in magnitude
(1) shunt field has the largest value amongst all the mentioned resistances. Ordinarily full voltage is applied across it. Its value decides the V^2/Rf loss. So to reduce V^2/Rf loss, it is advantageous to maximize the value of Rf , i.e the field resistance.
(2) Series field carries the full armature current, so its resistance value has to be as minimum as possible to minimize the Ia^2 R loss due to armature current Ia
(3) Armature resistance has to be as minimum as possible for the same reason mentioned under point no 2
They primarily differ in magnitude
(1) shunt field has the largest value amongst all the mentioned resistances. Ordinarily full voltage is applied across it. Its value decides the V^2/Rf loss. So to reduce V^2/Rf loss, it is advantageous to maximize the value of Rf , i.e the field resistance.
(2) Series field carries the full armature current, so its resistance value has to be as minimum as possible to minimize the Ia^2 R loss due to armature current Ia
(3) Armature resistance has to be as minimum as possible for the same reason mentioned under point no 2