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AP Physics C: E&M
11.7 Kirchhoff’s Junction Rule
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
AdvancedMCQMathematicalConceptual21.6k
A circuit schematic with three parallel vertical branches connected between a horizontal top wire and a horizontal bottom wire. The bottom wire has a ground symbol at its center and is labeled with a solid dot as node Z. The top wire has a solid dot at the center junction labeled as node X. The left vertical branch contains, from bottom to top, a battery symbol labeled \(\mathcal{E}_1\) with a longer upper line, a resistor zigzag labeled \(r_1\), a solid dot labeled as node W, and a resistor zigzag labeled \(R_1\) meeting the top wire. The middle vertical branch contains a single resistor zigzag labeled \(R_2\) connecting the top wire at node X to the bottom wire at node Z. The right vertical branch contains, from bottom to top, a battery symbol labeled \(\mathcal{E}_2\) with a longer upper line, a resistor zigzag labeled \(r_2\), a solid dot labeled as node Y, and a resistor zigzag labeled \(R_3\) meeting the top wire. No other labels, lines, text, or axes appear.
Schematic of the multi-loop circuit with labeled nodes W, X, Y, and Z.
A circuit consists of three vertical branches connected in parallel between an upper node labeled \(X\) and a lower grounded rail labeled \(Z\) (where \(V_Z = 0\text{ V}\)). The left branch contains a real battery with EMF \(\mathcal{E}_1 = 36\text{ V}\) and internal resistance \(r_1 = 1\text{ }\Omega\) (positive terminal facing upward) in series with an external resistor \(R_1 = 3\text{ }\Omega\), with node \(W\) located at the positive terminal between \(r_1\) and \(R_1\). The middle branch contains a single resistor \(R_2 = 4\text{ }\Omega\). The right branch contains a real battery with EMF \(\mathcal{E}_2 = 6\text{ V}\) and internal resistance \(r_2 = 1\text{ }\Omega\) (positive terminal facing upward) in series with an external resistor \(R_3 = 1\text{ }\Omega\), with node \(Y\) located at the positive terminal between \(r_2\) and \(R_3\). Which of the following correctly ranks the electric potentials \(V_W\), \(V_X\), \(V_Y\), and \(V_Z\) at the labeled nodes?

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