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title: "A two-stage resistor ladder network is connected across an ideal battery of potential difference \\(V_0\\). The network consists of two identical series resistors, \\(R_1\\) and \\(R_2\\), along the top rail and two identical shunt resistors, \\(R_3\\) and \\(R_4\\), connected across the rails as shown. All four resistors have the same resistance \\(R\\). Which of the following claims correctly compares the potential difference \\(V_1\\) across resistor \\(R_1\\) to the potential difference \\(V_2\\) across resistor \\(R_2\\), and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/118375/"
date_modified: "2026-08-04T08:09:46+00:00"
---

# A two-stage resistor ladder network is connected across an ideal battery of potential difference \(V_0\). The network consists of two identical series resistors, \(R_1\) and \(R_2\), along the top rail and two identical shunt resistors, \(R_3\) and \(R_4\), connected across the rails as shown. All four resistors have the same resistance \(R\). Which of the following claims correctly compares the potential difference \(V_1\) across resistor \(R_1\) to the potential difference \(V_2\) across resistor \(R_2\), and provides the correct physical justification?

A two-stage resistor ladder network is connected across an ideal battery of potential difference \(V_0\). The network consists of two identical series resistors, \(R_1\) and \(R_2\), along the top rail and two identical shunt resistors, \(R_3\) and \(R_4\), connected across the rails as shown. All four resistors have the same resistance \(R\). Which of the following claims correctly compares the potential difference \(V_1\) across resistor \(R_1\) to the potential difference \(V_2\) across resistor \(R_2\), and provides the correct physical justification?

![A schematic diagram of a DC circuit powered by an ideal battery labeled \(V_0\) on the left. The circuit consists of a top rail and a bottom return rail. Resistor \(R_1\) is located on the top rail in series. Following \(R_1\), a vertical branch contains shunt resistor \(R_3\) connecting the top rail to the bottom rail. To the right of this junction, resistor \(R_2\) is located on the top rail in series. Following \(R_2\), a second vertical branch contains shunt resistor \(R_4\) connecting the top rail to the bottom rail. All four resistors are labeled with resistance \(R\). Arrows indicate total current \(I_1\) flowing through \(R_1\) and current \(I_2\) flowing through \(R_2\). No other components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830986-wRbNTq.jpg)

- **A.** \(V_1 > V_2\), because \(R_1\) carries the total current supplied by the battery, whereas a portion of that current branches off through \(R_3\) before reaching \(R_2\).
- **B.** \(V_1 > V_2\), because the total equivalent resistance of the circuit reduces the voltage across successive resistors by equal constant fractions regardless of current branching.
- **C.** \(V_1 = V_2\), because identical resistors connected in series along the same rail must carry identical currents regardless of intermediate parallel branches.
- **D.** \(V_1 < V_2\), because the current increases as it moves further along the network due to the addition of parallel pathways.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118375/*