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title: "In the circuit shown, an ideal battery of EMF \\(\\varepsilon_0\\) is connected to a switch \\(S\\), two identical resistors each of resistance \\(R\\), and an initially uncharged capacitor of capacitance \\(C\\).  At time \\(t = 0\\), the switch is closed. Consider the following four currents in the circuit: – \\(I_1\\): the current through the battery at \\(t = 0^+\\) – \\(I_2\\): the current through resistor \\(R_2\\) as \\(t \\to \\infty\\) – \\(I_3\\): the current through capacitor \\(C\\) at time \\(t = \\tau\\), where \\(tau\\) is the time constant of the circuit – \\(I_4\\): the current through resistor \\(R_2\\) at \\(t = 0^+\\)  Which of the following correctly ranks the magnitudes of these currents from greatest to least?"
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url: "https://nerd-notes.com/ubq/121591/"
date_modified: "2026-08-23T05:24:11+00:00"
---

# In the circuit shown, an ideal battery of EMF \(\varepsilon_0\) is connected to a switch \(S\), two identical resistors each of resistance \(R\), and an initially uncharged capacitor of capacitance \(C\).

At time \(t = 0\), the switch is closed. Consider the following four currents in the circuit:
– \(I_1\): the current through the battery at \(t = 0^+\)
– \(I_2\): the current through resistor \(R_2\) as \(t \to \infty\)
– \(I_3\): the current through capacitor \(C\) at time \(t = \tau\), where \(tau\) is the time constant of the circuit
– \(I_4\): the current through resistor \(R_2\) at \(t = 0^+\)

Which of the following correctly ranks the magnitudes of these currents from greatest to least?

In the circuit shown, an ideal battery of EMF \(\varepsilon_0\) is connected to a switch \(S\), two identical resistors each of resistance \(R\), and an initially uncharged capacitor of capacitance \(C\).

At time \(t = 0\), the switch is closed. Consider the following four currents in the circuit:
- \(I_1\): the current through the battery at \(t = 0^+\)
- \(I_2\): the current through resistor \(R_2\) as \(t \to \infty\)
- \(I_3\): the current through capacitor \(C\) at time \(t = \tau\), where \(tau\) is the time constant of the circuit
- \(I_4\): the current through resistor \(R_2\) at \(t = 0^+\)

Which of the following correctly ranks the magnitudes of these currents from greatest to least?

![A rectangular schematic diagram of an electric circuit. On the left vertical branch is an ideal DC battery labeled \(\varepsilon_0\) with its longer positive plate on top, connected in series with an open switch labeled S above it. The top wire extends horizontally to the right through a resistor labeled \(R_1 = R\). After this resistor, the wire splits into two parallel vertical branches: the middle vertical branch contains a resistor labeled \(R_2 = R\), and the right vertical branch contains a parallel-plate capacitor labeled C. The bottom wire connects the bottom of both vertical branches back to the negative terminal of the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462651-ydBEXV.jpg)

- **A.** \(I_1 > I_3 > I_2 > I_4\)
- **B.** \(I_1 > I_2 > I_3 > I_4\)
- **C.** \(I_2 > I_1 > I_3 > I_4\)
- **D.** \(I_1 > I_2 > I_4 > I_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121591/*