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title: "Five identical resistors, each of resistance \\(R\\), are arranged in a bridge network between terminals \\(X\\) and \\(Y\\), as shown in the diagram. Four resistors form two parallel branches with intermediate nodes, and a fifth resistor \\(R_5\\) connects these two intermediate nodes. Which option correctly identifies the equivalent resistance \\(R_{eq}\\) between terminals \\(X\\) and \\(Y\\) and justifies why no current flows through resistor \\(R_5\\)?"
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url: "https://nerd-notes.com/ubq/118338/"
date_modified: "2026-08-04T08:09:34+00:00"
---

# Five identical resistors, each of resistance \(R\), are arranged in a bridge network between terminals \(X\) and \(Y\), as shown in the diagram. Four resistors form two parallel branches with intermediate nodes, and a fifth resistor \(R_5\) connects these two intermediate nodes. Which option correctly identifies the equivalent resistance \(R_{eq}\) between terminals \(X\) and \(Y\) and justifies why no current flows through resistor \(R_5\)?

Five identical resistors, each of resistance \(R\), are arranged in a bridge network between terminals \(X\) and \(Y\), as shown in the diagram. Four resistors form two parallel branches with intermediate nodes, and a fifth resistor \(R_5\) connects these two intermediate nodes. Which option correctly identifies the equivalent resistance \(R_{eq}\) between terminals \(X\) and \(Y\) and justifies why no current flows through resistor \(R_5\)?

![A schematic diagram of a bridge resistor network connected between two open-circle terminals labeled X on the left and Y on the right. Terminal X connects to a horizontal wire that splits into an upper path and a lower path. The upper path contains a resistor labeled R_1 followed by top node C, then a resistor labeled R_2 leading to a right-side junction node connected to terminal Y. The lower path contains a resistor labeled R_3 followed by bottom node D, then a resistor labeled R_4 leading to the same right-side junction node connected to terminal Y. A vertical resistor labeled R_5 is connected directly between top node C and bottom node D. All five resistors are drawn as standard zigzag resistor symbols. No other labels, text, or circuit elements appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830974-AC6iKq.jpg)

- **A.** Equivalent Resistance: \(R\) Justification: The electric potential at both ends of resistor \(R_5\) is equal, so the potential difference across it is zero.
- **B.** Equivalent Resistance: \(R\) Justification: The total resistance of the central branch is infinite because resistor \(R_5\) acts as an open circuit.
- **C.** Equivalent Resistance: \(\dfrac{5}{4}R\) Justification: The electric potential at both ends of resistor \(R_5\) is equal, so the potential difference across it is zero.
- **D.** Equivalent Resistance: \(\dfrac{R}{5}\) Justification: Current takes the path of least resistance through the outer branches, bypassing resistor \(R_5\) entirely.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118338/*