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title: "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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url: "https://nerd-notes.com/ubq/120440/"
date_modified: "2026-08-23T04:34:41+00:00"
---

# 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, \(\dfrac{I_1(0)}{I_1(\infty)}\)?

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, \(\dfrac{I_1(0)}{I_1(\infty)}\)?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459681-PqaH5W.jpg)

- **A.** \(\dfrac{2}{3}\)
- **B.** \(\dfrac{3}{4}\)
- **C.** \(\dfrac{8}{9}\)
- **D.** \(\dfrac{4}{3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120440/*