A long piece of uniform resistance wire is bent into a rectangle ABCD. A single ideal battery of rated value 9.0 V is inserted in side AB, while side CD contains a lumped resistor of resistance 18 Ω. A verbal description of an electric potential–versus–position graph obtained while moving a positive test charge once around the loop is given below.
• From point A to point B the graph shows a vertical upward step of +9.0 V.
• From point B through C to D the graph is a straight, uniformly sloping line that falls from +9.0 V at B to 0 V at D.
• From point D back to A the graph remains on the 0 V line.
A single loop is completed in the direction A→B→C→D→A.
Assume a test charge of magnitude 3.0 μC moves once around this loop in the indicated direction.
(a) Describe what physical element in the loop corresponds to (i) the vertical step AB and (ii) the sloping segment BCD of the potential graph. Explain your reasoning in each case.
(b) Determine the change in electric potential energy of the test charge as it moves from A to B.
(c) Determine the change in electric potential energy of the same test charge as it moves from B through C to D.
(d) Using your answers to parts (b) and (c), explain how the complete trip around the loop is consistent with the law of conservation of energy for the test charge.