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AP Physics 2
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current (DC) Circuits
11.3 Resistance, Resistivity, and Ohm’s Law
AdvancedMCQMathematicalProportional AnalysisConceptual12.8k
A schematic diagram of a DC circuit. On the far left, a vertical DC voltage source labeled emf \(\mathcal{E}\) is connected in series with an internal resistor labeled \(r = R\), surrounded by a light dashed rectangle. From the top of this battery assembly, a wire extends right through a resistor labeled \(R\) to a top node. From this node, the wire splits into two parallel vertical branches: Branch A on the left containing one resistor labeled \(2R\), and Branch B on the right containing two resistors connected in series, each labeled \(2R\). Both vertical branches connect at a bottom node, which connects via a horizontal wire back to the negative terminal of the battery assembly. No other labels, lines, text, or axes appear.
DC circuit network with internal resistance and external parallel branches.
A battery with electromotive force (emf) \(\mathcal{E}\) and internal resistance \(r = R\) is connected in a circuit with four external resistors, as shown in the schematic diagram. The circuit contains an external resistor of resistance \(R\) connected in series with a parallel network. The parallel network consists of two branches: Branch A contains a single resistor of resistance \(2R\), and Branch B contains two resistors connected in series, each with resistance \(2R\). What is the electric current flowing through Branch B, in terms of \(\mathcal{E}\) and \(R\)?

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