Electric current > Conductivity. Resistance. Sources of electromotive force > Problem 8.2.28

Statement

Without delving into the question of the origin of external forces, plot the potential of an open and closed circuit with resistance . On a section of the circuit of length , the force assigned to the unit of charge is equal to , and outside this section it is zero. What energy per unit charge is transmitted by the source of external forces in the section ?

Solution

The force per unit charge is equivalent to the electric field strength. Thus, the work done per unit charge by the force on a section of the circuit is , which is the same as the potential difference between points and . The graphs show potential difference between each point in the circuit and point . When the circuit is open (shown in red), the only change in potential is across the section of length . When the circuit is closed (shown in green), there is also potential drop of across the resistor. (Note the discontinuity in the potential between points and in the open circuit.)

Answer

See the figure.