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AP Physics C: E&M
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
11.4 Electric Power
AdvancedMCQMathematicalProportional Analysis16.9k
A rectangular circuit schematic. On the left vertical branch is a real battery enclosed by a dashed rectangular outline; inside the dashed box are an ideal battery symbol labeled \(\mathcal{E}\) with the longer line on top, in series with a small resistor symbol labeled \(r\). The top and bottom horizontal branches are solid connecting wires. On the right vertical branch is a variable resistor symbol, drawn as a resistor with a diagonal arrow pointing through its center toward the upper right, labeled \(R\). No other labels, lines, text, or axes appear.
A real battery connected to a variable load resistor.
A real battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected across a variable load resistor of resistance \(R\).

In Scenario 1, the load resistance is set to \(R_1\) such that the power delivered to the load is maximized. In Scenario 2, the load resistance is adjusted to \(R_2\) such that the operating efficiency, defined as the ratio of useful power delivered to the load to total power produced by the battery, is \(\dfrac{2}{3}\). What is the ratio \(\dfrac{P_2}{P_1}\) of the power delivered to the load in Scenario 2 to the power delivered to the load in Scenario 1?

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