# Torque Equation of DC Motor

The term torque as best explained by Dr. Huge d Young is the quantitative measure of the tendency of a force to cause a rotational motion, or to bring about a change in rotational motion. It is in fact the moment of a force that produces or changes a rotational motion.

The equation of torque is given by,

**torque of dc motor**is a very important parameter in this concern, and it’s of utmost importance to understand the

**torque equation of dc motor**for establishing its running characteristics.

To establish the torque equation, let us first consider the basic circuit diagram of a dc motor, and its voltage equation.
Referring to the diagram beside, we can see, that if E is the supply voltage, E_{b} is the back emf produced and I_{a}, R_{a} are the armature current and armature resistance respectively then the voltage equation is given by,

**torque equation of dc motor**we multiply both sides of equation (2) by I

_{a}.

_{a}

^{2}.R

_{a}is the power loss due to heating of the armature coil, and the true effective mechanical power that is required to produce the desired torque of dc machine is given by,

_{m}is related to the electromagnetic torque T

_{g}as,

Now equating equation (4) & (5) we get,

_{m}= T

_{g}- mechanical losses. This is the torque equation of dc motor. It can be further simplified as:

_{a}. The Torque equation of a dc motor can also be explained considering the figure below.

_{c}= I

_{a}/ A Therefore, force per conductor = f

_{c}= BLI

_{a}/A Now torque T

_{c}= f

_{c}.r = BLI

_{a}.r/A

_{a}.

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