What is meant by back e.m.f?

Back e.m.f.:

When the motor armature rotates,the conductors also rotate and hence cut the flux.In accordance with the laws of electromagnetic induction, e.m.f.is induced in them whose direction,as found by Fleming^,s Right-hand Rule,is in opposition to the applied voltage. Because of its opposite direction, it is referred to as counter e.m.f. or back e.m.f.E_b.

Fig:1

Prove that the gross power developed by a DC motor is maximum when the back e.m.f. (E_b) equals to the half of the applied voltage(V):

Back e.m.f.E_b=V_t-I_aR_a

Where V_t=applied terminal voltage, I_a=armature current, R_a=armature resistance

The gross mechanical power developed by a motor is Pm=VI_a-I2_aR_a

Differentiating both sides with respect to I_aand equating the result to zero,we get

dP_m/dI_a=V-2I_aR_a=0 Or, I_aR_a=V/2

As V=E_b+I_aR_a and I_aR_a=V/2 So E_b=V/2

Thus gross mechanical power developed by a motor is maximum when back e.m.f. is equal to half the applied voltage.

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