PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
A circuit contains two ideal batteries, three resistors, and three conducting branches. Battery A (emf 9.0 V) and resistor R₁ (2.0 Ω) are connected in series in the left branch. Battery B (emf 6.0 V) and resistor R₂ (3.0 Ω) are connected in series in the right branch. Resistor R₃ (4.0 Ω) joins the midpoints of the left and right branches, forming a central branch so that the overall network has three rectangular loops that share circuit elements.
Assume conventional current directions are initially chosen to be upward in the left and right branches and from left to right through R₃.
Answer the following questions about applying energy conservation to this network.
(a) Identify two loops that are independent of each other and justify why they are considered independent in the context of energy conservation.
(b) For one of the independent loops you selected in part (a), explain qualitatively why the algebraic sum of the potential differences around that loop must be zero even though the loop shares elements with other loops.
(c) Describe how the sign of the potential difference across each battery and resistor would be assigned if the assumed current directions listed in the stimulus were used in writing the loop equation. Explain the physical basis for your sign convention.
(d) Sketch a qualitative graph of electric potential versus position for a complete traversal of the left independent loop (beginning and ending at the negative terminal of Battery A). Clearly indicate the locations of each circuit element on the horizontal axis and the relative magnitudes of the potential changes on the vertical axis.