A circuit contains two batteries and two rectangular loops that share a single resistor
PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
A circuit contains two batteries and two rectangular loops that share a single resistor. A student labels one clockwise current in each loop, giving two unknown currents, and writes three loop equations: one for each individual loop and a third that traces the outer perimeter enclosing both loops. Which of the following best explains why solving the three equations does not yield any additional information beyond the first two equations?
(a) Because Kirchhoff’s loop rule can be applied only once to an entire circuit, any additional loop equations are invalid.
(b) The outer loop encloses no changing magnetic flux, so the induced emf is zero, making its loop equation trivial.
(c) The outer-perimeter equation is just the algebraic sum of the two individual-loop equations, so it is not an independent relation.
(d) The shared resistor means voltages on that element are counted twice, so a loop that includes both batteries gives an inconsistent equation.