---
title: "A circuit contains three identical resistors, each with a resistance of \\(12\\text{ }\\Omega\\). Two of the resistors are connected in parallel with each other, and this parallel pair is connected in series with the third resistor across an ideal DC voltage source. What is the total equivalent resistance of the three-resistor network?"
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url: "https://nerd-notes.com/ubq/120383/"
date_modified: "2026-08-23T04:34:25+00:00"
---

# A circuit contains three identical resistors, each with a resistance of \(12\text{ }\Omega\). Two of the resistors are connected in parallel with each other, and this parallel pair is connected in series with the third resistor across an ideal DC voltage source. What is the total equivalent resistance of the three-resistor network?

A circuit contains three identical resistors, each with a resistance of \(12\text{ }\Omega\). Two of the resistors are connected in parallel with each other, and this parallel pair is connected in series with the third resistor across an ideal DC voltage source. What is the total equivalent resistance of the three-resistor network?

![A schematic diagram of a DC circuit in a rectangular loop. On the left vertical segment is an ideal DC voltage source with long and short parallel lines, labeled \(\Delta V\). A wire extends from the top of the source to the right, passing through a zigzag resistor labeled \(R_1 = 12\text{ }\Omega\). The wire then splits at a junction into two parallel horizontal branches: the top branch contains a zigzag resistor labeled \(R_2 = 12\text{ }\Omega\), and the bottom branch contains a zigzag resistor labeled \(R_3 = 12\text{ }\Omega\). The two branches rejoin at a right-hand junction. The wire continues downward and returns along the bottom horizontal segment to the bottom terminal of the voltage source. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1787459664-pVRXoc.jpg)

- **A.** \(8.0\text{ }\Omega\)
- **B.** \(18\text{ }\Omega\)
- **C.** \(24\text{ }\Omega\)
- **D.** \(36\text{ }\Omega\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120383/*