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AP Physics 2
11.8 Resistor-Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current (DC) Circuits
AdvancedMCQMathematicalConceptual13.2k
A circuit schematic is drawn in black lines on a white background. On the left side is a vertical branch with an ideal battery labeled \(\varepsilon\), with the longer positive plate on top. Connected from the positive terminal of the battery, a top horizontal wire extends to an open single-pole single-throw switch labeled \(S\), followed by a resistor labeled \(R_1 = R\). To the right of resistor \(R_1\), the wire splits at a node into two parallel branches. The top parallel branch contains a resistor labeled \(R_2 = 3R\). The bottom parallel branch contains a resistor labeled \(R_3 = 6R\) connected in series with a parallel-plate capacitor labeled \(C\). The two parallel branches rejoin at a right node, which connects to a bottom horizontal wire returning to the negative terminal of the battery. No other labels, lines, text, or circuit components appear.
Circuit containing a battery, switch, three resistors, and an initially uncharged capacitor.
In the circuit shown, an ideal battery of electromotive force \(\varepsilon\) is connected to an open switch \(S\), three resistors with resistances \(R_1 = R\), \(R_2 = 3R\), and \(R_3 = 6R\), and an initially uncharged capacitor of capacitance \(C\). Switch \(S\) is closed at time \(t = 0\). What is the ratio of the current through resistor \(R_1\) immediately after switch \(S\) is closed to the current through resistor \(R_1\) long after switch \(S\) is closed, \(\dfrac{I_1(0)}{I_1(\infty)}\)?

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