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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
AdvancedMCQGraphicalProportional Analysis19.5k
Grayscale schematic of an electrical circuit on a white background. On the far left, a vertical branch contains an ideal DC battery symbol labeled \(\mathcal{E}\), with a longer horizontal line on top and a shorter, thicker line on bottom. A top wire extends rightward from the battery, containing a zigzag resistor symbol labeled \(R\), and terminates at a solid dot labeled Node 1. Extending vertically downward from Node 1 to a bottom horizontal rail is a narrow rectangle representing a slide-wire resistor of total resistance \(R\) and length \(L\); a horizontal arrow labeled \(x\) points from the left into the rectangle at height \(x\) above the bottom rail. From Node 1, the top wire continues rightward through a zigzag resistor symbol labeled \(R\) to a solid dot labeled Node 2. Extending vertically downward from Node 2 to the bottom rail is a branch that splits into two parallel vertical sub-paths: the left sub-path contains two equal parallel plates labeled \(C\), and the right sub-path contains a zigzag resistor symbol labeled \(R\); the two sub-paths rejoin before meeting the bottom rail. The bottom rail is a continuous solid line returning to the negative terminal of the battery. No other labels, lines, text, or axes appear.
Circuit schematic showing the battery, slide-wire resistor, and ladder network.
In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with a resistor of resistance \(R\). This source feeds a two-stage ladder network consisting of an upper rail with two nodes and a common lower rail:

- At Node 1, a vertical branch contains a uniform slide-wire resistor of total length \(L\) and total resistance \(R\). A sliding contact at distance \(x\) (where \(0 \le x \le L\)) from the lower rail sets the active resistance of this branch between Node 1 and the lower rail to \(R_1(x) = R\left(\dfrac{x}{L}\right)\).
- A horizontal resistor of resistance \(R\) connects Node 1 to Node 2.
- At Node 2, a vertical branch contains an initially uncharged capacitor of capacitance \(C\) connected in parallel with a fixed resistor of resistance \(R\).

Which of the following graphs best represents the steady-state current \(I\) through the fixed resistor at Node 2 as a function of the slider position \(x\)?

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