Four students discuss how to assign algebraic signs to potential differences while analysing circuits. Consider each of their statements.
I. “When you go through any resistor in the direction of current, the potential difference is negative because the current loses energy.”
II. “If you traverse a battery from its negative terminal to its positive terminal, the potential difference you record is positive.”
III. “Reversing the traversal direction around a loop flips the sign of every term in the loop sum, so the overall loop equation remains valid.”
IV. “If two batteries are oriented in the same direction in a loop, the loop sum of potential differences cannot be zero, so Kirchhoff’s loop rule fails.”
(a) Evaluate statement I. Indicate whether it is correct, partially correct, or incorrect, and provide a clear justification.
(b) Evaluate statement II in the same manner as part (a).
(c) Evaluate statement III in the same manner as part (a).
(d) Evaluate statement IV in the same manner as part (a).
(e) Using your evaluations from parts (a)–(d), formulate a concise criterion that guarantees the algebraic sum of potential differences around any closed loop is zero. Support your criterion with reasoning.