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title: "An ideal battery of potential difference \\(\\Delta V\\) is connected to a circuit containing four ideal ammeters (\\(A_1\\), \\(A_2\\), \\(A_3\\), \\(A_4\\)) and four resistors. Resistor \\(R_1\\) has resistance \\(2R\\), while resistors \\(R_2\\), \\(R_3\\), and \\(R_4\\) each have resistance \\(R\\). Ammeter \\(A_1\\) measures the total current leaving the battery, ammeter \\(A_2\\) is in series with \\(R_1\\), ammeter \\(A_3\\) is in series with \\(R_2\\), and ammeter \\(A_4\\) is in series with \\(R_3\\). Which of the following correctly ranks the currents \\(I_1\\), \\(I_2\\), \\(I_3\\), and \\(I_4\\) measured by ammeters \\(A_1\\), \\(A_2\\), \\(A_3\\), and \\(A_4\\), respectively?"
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url: "https://nerd-notes.com/ubq/117510/"
date_modified: "2026-08-04T06:52:28+00:00"
---

# An ideal battery of potential difference \(\Delta V\) is connected to a circuit containing four ideal ammeters (\(A_1\), \(A_2\), \(A_3\), \(A_4\)) and four resistors. Resistor \(R_1\) has resistance \(2R\), while resistors \(R_2\), \(R_3\), and \(R_4\) each have resistance \(R\). Ammeter \(A_1\) measures the total current leaving the battery, ammeter \(A_2\) is in series with \(R_1\), ammeter \(A_3\) is in series with \(R_2\), and ammeter \(A_4\) is in series with \(R_3\). Which of the following correctly ranks the currents \(I_1\), \(I_2\), \(I_3\), and \(I_4\) measured by ammeters \(A_1\), \(A_2\), \(A_3\), and \(A_4\), respectively?

An ideal battery of potential difference \(\Delta V\) is connected to a circuit containing four ideal ammeters (\(A_1\), \(A_2\), \(A_3\), \(A_4\)) and four resistors. Resistor \(R_1\) has resistance \(2R\), while resistors \(R_2\), \(R_3\), and \(R_4\) each have resistance \(R\). Ammeter \(A_1\) measures the total current leaving the battery, ammeter \(A_2\) is in series with \(R_1\), ammeter \(A_3\) is in series with \(R_2\), and ammeter \(A_4\) is in series with \(R_3\). Which of the following correctly ranks the currents \(I_1\), \(I_2\), \(I_3\), and \(I_4\) measured by ammeters \(A_1\), \(A_2\), \(A_3\), and \(A_4\), respectively?

![A rectangular DC circuit schematic. On the left vertical wire, an ideal DC battery is drawn with potential difference labeled \(\Delta V\), positive terminal on top. The top wire extends rightward to a junction J1. Ammeter \(A_1\), drawn as a circle with an A inside, is located on the top wire between the battery and junction J1. At junction J1, the circuit splits into two parallel vertical branches. The left parallel branch contains ammeter \(A_2\) and resistor \(R_1\) (labeled \(2R\)) in series. The right parallel branch begins with ammeter \(A_3\) in series with resistor \(R_2\) (labeled \(R\)), which then leads to a second junction J2. At junction J2, the right branch splits into two sub-parallel vertical paths: the left sub-path contains ammeter \(A_4\) and resistor \(R_3\) (labeled \(R\)) in series, while the right sub-path contains resistor \(R_4\) (labeled \(R\)). The two sub-paths rejoin at junction J3 and connect back to the main return path at junction J4 on the bottom wire, which returns to the negative terminal of the battery. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826348-050Zji.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117510/*