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AP Physics 2
11.7 Kirchhoff’s Junction Rule
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current (DC) Circuits
AdvancedMCQMathematicalConceptual18.9k
A schematic diagram of a circuit with three vertical branches connected in parallel by a top horizontal wire and a bottom horizontal wire. A filled black circle labeled X is located at the center of the top horizontal wire where the middle branch connects. A filled black circle labeled Y is located at the center of the bottom horizontal wire where the middle branch connects. The left vertical branch consists of a resistor labeled \(R\) below a long-and-short parallel line battery symbol labeled \(\mathcal{E}\), with the longer line at the top. The middle vertical branch consists of a single resistor labeled \(R\). The right vertical branch consists of a resistor labeled \(R\) below a long-and-short parallel line battery symbol labeled \(3\mathcal{E}\), with the longer line at the top. No other components, labels, or decorative lines appear.
A multi-loop circuit with three parallel branches.
A multi-loop circuit consists of three vertical parallel branches connected between a top horizontal wire containing node \(X\) and a bottom horizontal wire containing node \(Y\). The left branch contains an ideal battery of emf \(\mathcal{E}\) in series with a resistor of resistance \(R\), with the positive battery terminal connected toward node \(X\). The middle branch contains only a single resistor of resistance \(R\). The right branch contains an ideal battery of emf \(3\mathcal{E}\) in series with a resistor of resistance \(R\), with its positive battery terminal also connected toward node \(X\). What is the electric potential difference \(V_X - V_Y\) between node \(X\) and node \(Y\)?

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