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AP Physics C: E&M
11.5 Compound Direct Current Circuits
AdvancedMCQMathematicalProportional Analysis24.1k
A circuit schematic of a semi-infinite ladder network. On the left are two open terminal circles arranged vertically. From the top terminal, a horizontal wire extends rightward, containing three series resistor symbols in a row, each labeled \(R_1\). From the bottom terminal, a straight horizontal wire extends rightward. Three vertical branches connect the top wire to the bottom wire, positioned after each series resistor; each vertical branch contains a resistor symbol labeled \(R_2\). To the right of the third stage, both the top and bottom wires terminate with three horizontal dots \(\dots\) indicating that the pattern of series and shunt resistors repeats infinitely to the right. No other labels, lines, text, or axes appear.
Infinite ladder network of resistors.
An infinite ladder network of resistors is constructed from identical stages, as shown in the diagram. Each stage contains a series resistor of resistance \(R_1\) along the upper wire and a shunt resistor of resistance \(R_2\) connecting the upper and lower wires. In the limit where the shunt resistance is much greater than the series resistance (\(R_2 \gg R_1\)), which of the following expressions best represents the equivalent resistance \(R_{eq}\) between the input terminals?

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