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title: "In the circuit shown, an ideal battery of constant voltage \\(V_0\\) is connected in series with an open switch \\(S\\) and a resistor of resistance \\(R\\). This combination is connected across a parallel network consisting of a resistor of resistance \\(3R\\) in one branch and two uncharged, identical capacitors, each of capacitance \\(C\\), connected in series with each other in the second branch. At time \\(t = 0\\), switch \\(S\\) is closed. Which of the following expressions represents the total current \\(I(t)\\) supplied by the battery as a function of time \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/118442/"
date_modified: "2026-08-04T08:10:07+00:00"
---

# In the circuit shown, an ideal battery of constant voltage \(V_0\) is connected in series with an open switch \(S\) and a resistor of resistance \(R\). This combination is connected across a parallel network consisting of a resistor of resistance \(3R\) in one branch and two uncharged, identical capacitors, each of capacitance \(C\), connected in series with each other in the second branch. At time \(t = 0\), switch \(S\) is closed. Which of the following expressions represents the total current \(I(t)\) supplied by the battery as a function of time \(t \ge 0\)?

In the circuit shown, an ideal battery of constant voltage \(V_0\) is connected in series with an open switch \(S\) and a resistor of resistance \(R\). This combination is connected across a parallel network consisting of a resistor of resistance \(3R\) in one branch and two uncharged, identical capacitors, each of capacitance \(C\), connected in series with each other in the second branch. At time \(t = 0\), switch \(S\) is closed. Which of the following expressions represents the total current \(I(t)\) supplied by the battery as a function of time \(t \ge 0\)?

![A rectangular schematic diagram of an electric circuit. On the left vertical wire, an ideal battery is oriented vertically with positive terminal on top, labeled V_0. An open switch labeled S is located on the top horizontal wire, to the right of the battery. To the right of switch S on the top horizontal wire is a resistor labeled R. Beyond resistor R, the top wire reaches a junction node that splits into two vertical parallel branches. The middle vertical branch contains a resistor labeled 3R. The right vertical branch contains two capacitors connected in series, each labeled C, arranged vertically one above the other. Both parallel branches rejoin at a bottom junction node, which connects via a bottom horizontal wire back to the negative terminal of the battery. An arrow labeled I(t) points to the right along the top wire between the battery and switch S. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831007-k93d3O.jpg)

- **A.** \(I(t) = \dfrac{V_0}{4R}\left(1 + 3e^{-\frac{t}{8RC}}\right)\)
- **B.** \(I(t) = \dfrac{V_0}{4R}\left(1 + 3e^{-\frac{t}{2RC}}\right)\)
- **C.** \(I(t) = \dfrac{V_0}{4R}\left(4 - 3e^{-\frac{8t}{3RC}}\right)\)
- **D.** \(I(t) = \dfrac{V_0}{4R}\left(1 + 3e^{-\frac{8t}{3RC}}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118442/*