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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
IntermediateMCQMathematicalConceptual16.8k
A schematic diagram of a two-loop direct current circuit on a plain white background. The circuit features three vertical parallel branches connected at top and bottom horizontal wires. The left branch contains an ideal DC battery labeled \(\mathcal{E}_1 = 16\text{ V}\) with its longer positive terminal on top, connected in series below a resistor labeled \(R_1 = 4\ \Omega\). The middle branch contains a single vertical resistor labeled \(R_2 = 4\ \Omega\). The right branch contains a resistor labeled \(R_3 = 2\ \Omega\) connected in series above an ideal DC battery labeled \(\mathcal{E}_2 = 4\text{ V}\), which has its longer positive terminal on top. Black dots mark the top and bottom junction nodes. No other text, lines, arrows, or labels appear.
Two-loop DC circuit schematic.
A circuit contains two loops connected by a top junction and a bottom junction, as shown in the schematic. The left branch contains an ideal battery of emf \(\mathcal{E}_1 = 16\text{ V}\) in series with resistor \(R_1 = 4\ \Omega\). The middle branch contains resistor \(R_2 = 4\ \Omega\). The right branch contains resistor \(R_3 = 2\ \Omega\) in series with an ideal battery of emf \(\mathcal{E}_2 = 4\text{ V}\) directed upward. What is the potential difference across resistor \(R_3\), and what is the direction of the current through the right-hand branch?

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