Electrical Engineering ⇒ Topic : Back E.M.F.

The operation of a dc motor depends on the principle that a current carrying conductor of length 1, placed in, and at right angles to, a magnetic field (B)tends to experience a force F = I (1 x B), which moves the conductor at right angles to the direction of the field, as shown in Fig.  The magnetic field between two poles N and S is shown in Fig (a). A cross-section of a current carrying conductor is shown in Fig.(b) along with the direction of the flux loops around it.If the conductor is placed between the two magnetic poles as shown in Fig.(c), both the fields will be distorted.Above the conductor, the field is weakened and the conductor tends to move upwards.The force exerted upwards depends on the intensity of the main magnetic field and the magnitude of current. If the direction of current through the conductor is reversed as shown in Fig.(d), the direction of the field around the conductor is reversed. The field below the conductor is now weakened, and the conductor tends to move downwards. The principle

              Force acting on a current carrying conductor in a magnetic field

of operation of a dc motor having a two-conductor armature is illustrated in Fig. In actual practice, a dc motor has many coils in its armature. The force, F that acts on a current carrying conductor is given by the equation

                            Magnetic field of a two conductor armature

                                         F = B.Ι .l Newtons

where, B is the magnetic field intensity in Web/m², I is the current in amperes and 1 is the length of the conductor in meters. The above equation gives the magnitude of the force where direction is given by the Fleming's Left Hand Rule. Each armature conductor experiences a force F which tends to rotate the armature. If there are a large number of conductors, the forces in individual conductors collectively produce a driving torque (or twisting moment) which makes the armature to rotate.

          As mentioned earlier, the same dc machine can be used both as a generator and as a motor. As a generator, it generates emf given by the (which can be written as

                                              E = V + l_aR_a

where, E = generated emf, V = terminal voltage, l_a = armature current and R_a= armature resistance.

         When the machine is operating as a motor, it takes in electrical energy and gives out mechanical energy. Here, the emf across the armature, E is less than the applied voltage V and the direction of the armature current la is the reverse of the direction of current when the machine acts as a motor.

Here, the emf across the armature E is the generated emf because of the rotation of the armature conductors in the magnetic field. The direction of this generated emf can be obtained by using the Fleming's Right Hand Rule, and is in opposition to the applied voltage. For this reason, it is called the back emf (E_b), and the is rewritten as

                                           V = E_b + i_ar_a

  The circuit of a dc motor is shown in Fig.