A single closed loop contains two identical resistors
PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity
Problem
A single closed loop contains two identical resistors, labelled R1 and R2, connected sequentially between points X, Y, and Z in that order (X → Y → Z → X). A single ideal battery of emf E can be inserted at any one of the three segments and oriented arbitrarily. Conventional current is observed to flow in the direction X → Y → Z → X.
A student claims: “As long as the battery is somewhere in the loop, the algebraic sum of potential differences around the loop will always be zero, no matter which way the battery faces.”
(a) Evaluate the student’s claim for the case in which the battery is placed between points X and Y with its positive terminal toward X (opposite the direction of the current through that segment). Explain whether the loop sum equals zero and why.
(b) Evaluate the claim for the same placement of the battery but with its positive terminal toward Y (i.e., in the same direction as the current through that segment).
(c) Generalise your reasoning to any placement of a single battery in a simple resistive loop. State a condition that the battery’s orientation must satisfy relative to the direction of conventional current so that the closed-loop sum of potential differences is zero, and justify your condition thoroughly.