An electric circuit contains a single ideal battery, two identical resistors labelled R, and ideal connecting wires arranged in one simple loop. A student begins at point A on the negative terminal of the battery and walks clockwise once around the loop while recording the electric potential V at successive positions. The resulting potential–position graph is described verbally below.
• Segment AB: the graph rises vertically from 0 V to +12 V.
• Segment BC: the graph decreases linearly from +12 V to +6 V.
• Segment CD: the graph is horizontal at +6 V.
• Segment DE: the graph decreases linearly from +6 V to 0 V.
• Segment EA: the graph is horizontal at 0 V and returns to the starting point.
Positions B and D coincide with the physical locations of the two resistors; the other segments correspond to the battery or ideal wires.
(a) For each of the five graph segments (AB, BC, CD, DE, EA) identify the specific circuit element it represents and justify your choice based on the shape or orientation of that segment.
(b) Explain why the magnitudes of the potential drops across segments BC and DE are equal, given that the two resistors are identical.
(c) Describe how the overall shape of the graph demonstrates conservation of energy for a charge completing one loop of the circuit.
(d) Suppose the resistor at position D is replaced by a resistor of resistance 2R while the other components remain unchanged. Qualitatively sketch (no numerical scale required) how segment DE of the potential–position graph would change, and explain the physical reasoning for your sketch.