JEE Main & Advanced Physics Electro Magnetic Induction dc Motor

It is an electrical machine which converts electrical energy into mechanical energy.

(1) Principle : It is based on the fact that a current carrying coil placed in the magnetic field experiences a torque. This torque rotates the coil.

(2) Construction : It consists of the following components figure..

ABCD = Armature coil, \[{{S}_{1}},\,{{S}_{2}}=\]split ring comutators 

\[{{B}_{1}},\,\,{{B}_{2}}=\] Carbon brushes, N, S = Strong magnetic poles

(3) Working : Force on any arm of the coil is given by \[\vec{F}=i(\vec{l}\times \vec{B})\] in fig., force on AB will be perpendicular to plane of the paper and pointing inwards. Force on CD will be equal and opposite. So coil rotates in clockwise sense when viewed from top in fig. The current in AB reverses due to commutation keeping the force on AB and CD in such a direction that the coil continues to rotate in the same direction.

(4) Back emf in motor : Due to the rotation of armature coil in magnetic field a back emf is induced in the circuit. Which is given by \[e=E-iR\].

Back emf directly depends upon the angular velocity \[\omega \]of armature and magnetic field B. But for constant magnetic field B, value of back emf e is given by  \[e\propto \omega \] or  \[e=k\omega \]\[(e=NBA\,\omega \sin \omega t)\]

(5) Current in the motor :  \[i=\frac{E-e}{R}=\frac{E-k\omega }{R}\]; When motor is just switched on i.e. \[\omega =0\] so \[e=0\] hence \[i=\frac{E}{R}=\text{maximum}\] and at full speed, \[\omega \] is maximum so back emf e is maximum and i is minimum. Thus, maximum current is drawn when the motor is just switched on which decreases when motor attains the speed.

(6) Motor starter : At the time of start a large current flows through the motor which may burn out it. Hence a starter is used for starting a dc motor safely. Its function is to introduce a suitable resistance in the circuit at the time of starting of the motor. This resistance decreases gradually and reduces to zero when the motor runs at full sped.

The value of starting resistance is maximum at time \[t=0\] and its value is controlled by spring and electromagnetic system and is made to zero when the motor attains its safe speed.

(7) Mechanical power and Efficiency of dc motor :

Efficiency \[\eta =\frac{{{P}_{mechanical}}}{{{P}_{\sup plied}}}=\frac{{{P}_{out}}}{{{P}_{in}}}\]\[=\frac{e}{E}=\frac{\text{Back e}\text{.m}\text{.f}\text{.}}{\text{Supply voltage}}\]

(8) Uses of dc motors : They are used in electric locomotives, electric ears, rolling mills, electric cranes, electric lifts, dc drills, fans and blowers, centrifugal pumps and air compressors, etc.