## Torque Equation for DC Motor

Torque is a rotational force that helps for rotating the armature of DC motor. Torque is produced by electromagnetic effect. In simple words we can say that, when a conductor carrying current placed in a magnetic field or flux a mechanical force experienced by the conductors and conductor moves in a particular direction. In this article we will drive torque equation for dc motor.

Torque is measured by the product of force F and radius r.

T = F × r

Let us suppose that the DC machine working as a motor

P = number of poles

Φ = Flux per pole in Weber (Wb)

B = Flux density in Tesla or Wb/m2

r = radius of armature in meters

l = length of the conductor in meters

i = current flowing through the conductor

Now we will calculate force on each conductor

F = Bil newtons

Torque due to one conductor

T = F ×r Newton-meter (Nm)

In above equation, we have find torque due to one conductor. But if the number conductors are more than one then the above equation is multiplied by Z. Z denotes the total number armature conductors.

Now total armature torque developed is

T = Z Fr Newton-meter (Nm)

If i is the current in each conductor then total armature conductor is Ia and number of parallel paths are A, then

Conclusion:- From the above torque equation for dc motor, we arrived at a conclusion, which are discussed below:-

The torque developed is directly proportional to the flux per pole. If the flux is increased torque is also increased.

The torque developed is directly proportional to the number of armature conductor.

Torque depends on number of poles.

The torque depends on armature current or current flowing through the armature conductor.

Torque is inversely proportional to the number of parallel path.