A battery of emf and internal resistance is driving a motor. The motor is lifting a 2.0-N object at constant speed . Assuming no power losses, we have to find (a) the current i in the circuit and (b) the potential difference V across the terminals of the motor. (c) We have to discuss the fact that there are two solutions to the problem.

Solution:             Click For PDF Version

(a)

The rate at which electrical energy in the motor is being used in gaining gravitational potential energy is

Let the current in the circuit be i A. The power supplied by the battery is

It is equal to the Joule heat in the internal resistance of the battery plus the power spent at the motor in lifting the object. That is

We thus have the following equation for the current

Roots of this quadratic equation are

(b) and (c)

There are therefore two solutions for this problem.

When the current in the circuit is 3.41 A the potential difference across the terminals of the motor will be

When the current in the circuit is 0.586 A the potential difference across the terminals of the motor will be