Dec 9, 2014

DC Motor Voltage Equation and Power Equation


Voltage Equation:

Consider a shunt wound motor shown in Fig.
Let,         V = applied voltage
                Eb = back e.m.f.
                Ia = armature current
               Ra = armature resistance

Meanwhile back e.m.f. Eb acts in reverse to the applied voltage V, the net voltage through the armature circuit is V-Eb. Now the armature current Ia is given by;
              Ia = V-Eb/Ra
               V = Eb + Ia Ra       ====> (1)
This is known as voltage equation of the d.c. motor.

Power Equation:

If the above Eqn. (1) is multiplied with Ia throughout, we get,
              VIa = Eb Ia + I2a Ra

This is said to be a power equation of the d.c. motor.

          VIa = armature input (electric power supplied to armature)
          EbIa = armature output (power developed by armature)
          Ia Ra = armature Cu loss (electric power wasted in armature)

Therefore out of the armature input, a small portion (about 5%) is wasted as I2aRa and the remaining portion EbIa is changed into mechanical power within the armature.


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