A dc motor works on the principle that a current carrying coil, when placed in a magnetic field experiences a torque. The arrangement consists of a coil suspended in a region of magnetic field. When a current is passed through the coil, it experiences torque and starts rotating. A simple arrangement is shown below.

The coil rotates under the action of torque. The current is supplied to the coil by an arrangement of two sliding contacts and a split ring. As the coil rotates, the magnetic flux linked with the coil changes. This leads to production of an induced emf `epsilon` in the coil. By Lenz's law, the induced emf opposes the applied voltage and therefore, it is called back emf. If R is the resistance in the coil, the current `i` flowing through the coil at any instant is `i=(V-epsilon)/(R)`. The back emf is developed due to induction and it is directly proportional to speed of rotation and it is directly proportional to speed of rotation of the motor. There is a continuous power loss `i^(2)R` in the motor, in form of heat.
In a dc motor, V is applied voltage, `epsilon` is back emf, i is current through the motor and R is resistance of the coil. mechanical power output of the motor is

Options

A. a.`i^(2)R`
B. b.`epsilon i`
C. c.`(V-epsilon)i`
D. d.`epsiloni-i^(2)R`

Answer

B