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AP Physics C: E&M
11.5 Compound Direct Current Circuits
11.4 Electric Power
AdvancedMCQMathematicalConceptual14.8k
A Cartesian coordinate system with a horizontal axis labeled \(I\) and a vertical axis labeled \(\Delta V\). The origin is at the intersection of the two perpendicular axes. A single straight solid line with a negative slope starts on the vertical axis at a tick mark labeled \(V_0\) and extends downward and to the right into the first quadrant. An annotation next to the line indicates a slope of \(-s\). No other labels, lines, text, or axes appear.
Plot of terminal voltage \(\Delta V\) versus current \(I\) for the nonideal battery.
A student performs an experiment to characterize a nonideal battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) by connecting it across a variable load resistor. The student measures the battery's terminal voltage \(\Delta V\) as a function of the output current \(I\) delivered to the load, obtaining a linear best-fit line with vertical intercept \(V_0\) and slope \(-s\), where \(s > 0\). Which of the following expressions correctly gives the internal resistance \(r\) of the battery and the maximum power \(P_{\text{max}}\) that the battery can deliver to the load resistor?

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