---
title: "Equivalent resistance between A and B"
subject: "Basic Electrical Engineering"
chapter: 2
key: "semester_1/basic_electrical_engineering:equivalent-resistance-24-8-8"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/equivalent-resistance-24-8-8
site: BCT Engineering
---

# Equivalent resistance between A and B

Basic Electrical Engineering · Chapter 2: DC circuits

- Asked in: 2073 Shrawan, 4 marks
- Video: [Equivalent Resistance (Solved Problem 1)](https://www.youtube.com/watch?v=jTjEMBe4NpY) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/equivalent-resistance-24-8-8
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-2

## Question

Find the equivalent resistance between A and B for the network shown in figure below. [Figure: 24 Ω resistor across the top; two 8 Ω resistors in the middle meeting at terminal A; terminal B at the bottom.]

## Short answer

The wire shorts the 24 Ω resistor, so it carries no current. The two 8 Ω resistors are in parallel between terminals A and B. Equivalent resistance RAB = 8 Ω || 8 Ω = 4 Ω.

## Answer

#### Reading the figure
The 24 Ω and the 8 Ω pair are connected between the left and right nodes X and Y. The outer wire joins X to Y directly and terminal B is on this wire, so X, Y and B are all the same point. Terminal A is the middle point between the two 8 Ω resistors.

```text
   X ---[24]--- Y        X = Y = B (joined by the wire)
   X --[8]--A--[8]-- Y
```

#### Analysis
- The 24 Ω resistor is connected across X and Y, which are shorted together, so it carries no current and can be ignored.
- Between A and B: the left 8 Ω (A to X) and the right 8 Ω (A to Y) both end at point B.

R_AB = 8 ∥ 8 = (8 × 8)/(8 + 8) = 4 Ω

**Answer: R_AB = 4 Ω**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does the 24 Ω resistor carry no current?
   A. Its value is too large to matter
   B. It is connected across X and Y, which are joined by a wire
   C. It is in series with an open circuit
   D. It is in parallel with a current source
   Answer: B. A wire between X and Y shorts the 24 Ω, so no current flows through it. (Key point: Shorted resistor)

2. Terminal B is on the wire joining X and Y, so
   A. X, Y and B are the same point
   B. B is at a higher voltage than X
   C. B is in series with A
   D. B is isolated from X and Y
   Answer: A. A wire has zero resistance, so every point on it is at the same potential. (Key point: Same-point nodes)

3. Both 8 Ω resistors go from A to the same point B. R_AB is
   A. 16 Ω (8 in series with 8)
   B. 8 Ω
   C. 12 Ω
   D. 4 Ω (8 in parallel with 8)
   Answer: D. Both have the same two end points (A and B), so they are in parallel: 8 x 8/16 = 4 Ω. (Key point: Combination)

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