A V ideal battery is connected to a resistive network composed of five resistors that…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits
Problem
A 12V ideal battery is connected to a resistive network composed of five resistors that create three distinct junctions, labeled A, B, and C. Starting from the positive terminal of the battery, current reaches junction A where it splits into two paths. Path 1 carries current I1 through a 4Ω resistor to junction B. Path 2 carries current I2 through a 6Ω resistor to junction C. Junctions B and C are interconnected by a 3Ω resistor that carries current I3 from B toward C (positive if toward C). From junction B, current I4 returns to the negative battery terminal through a 5Ω resistor. From junction C, current I5 returns to the negative battery terminal through a 7Ω resistor. All conductors are ideal and the only potential changes occur across the battery and the resistors.
(a) Write a current-conservation equation for each of the three junctions A, B, and C in terms of the currents I1 through I5 defined above.
(b) Assign the electric potential at the negative battery terminal to be 0V. Express each current I1–I5 in terms of the potential differences between the appropriate junctions and the given resistances.
(c) Combine your results from parts (a) and (b) to determine the numerical values (including sign) of all five currents.
(d) Based on your solved current directions and magnitudes, state whether electrical energy is delivered to or absorbed by the 3Ω resistor, and calculate the rate at which energy is transferred in that resistor.