Question
in a DC motor why and how the gain K is affected by the amaurtue resistant and induance ? whats the actual units for K.

For tau is affect just by taking induance over resistant? thanks

The gain K appears in DC motor emf equation as E = K and in torque equation as T = KI where is the speed of rotation in rad/s and I is the armature current.

The gain K = PZ/2a where P is the number of poles, Z is the number of armature conductors, is the flux per pole and a is the number of parallel paths. So clearly K does not depend on armature resistance R or inductance L and is not affected by them. Changing R and L will change other motor parameters but not K.

The unit of K is Volt-sec/radian or Newton-metre/Ampere. Both are dimensionally equivalent.

Tau or = L/R is the electrical time constant of the motor and it depends on armature resistance and inductance.

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