Torque Equation of D.C. Motor

In D.C. machine it is seen that the machine torque is uniform for given flux per pole and armature current. Torque is defined as the product of force with its radial distance at which it acts.

T = F × r

But

F = BIL...Newton

where,

B = flux density in Wb/m2
I = current through armature conductor in Amp
L = Length of armature conductor
r = radius of armature drum.

Considering,

P = Total number of poles
Φ = Flux cut per pole in Wb
Z = Total number of armature conductor
A = Number of parallel paths
I_a = Armature current

Substituting the values of B and I we get,

Since Z are the total number of conductors, therefore total torque is given by

This is known as torque equation of D.C. motor. But P, Z and A are constant hence,

T ∝ ΦIa

Thus the torque produced by a D.C. Motor is directly proportional to main flux Φ as well as armature current Ia.