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Found in: Page 796

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# A total resistance of 3.00 Ω is to be produced by connecting an unknown resistance to a 12.0 Ω resistance.What must be the value of the unknown resistance, and (b) Should it be connected in series or in parallel?

1. The value of the unknown resistance is ${R}^{\text{'}}=4.00\text{Ω}$
2. The unknown resistance should be connected in parallel.
See the step by step solution

## Step 1: Given

${R}_{eq}=3.00\text{Ω}\phantom{\rule{0ex}{0ex}}R=12.0\text{Ω}$

## Step 2: Determining the concept

It can be predicted whether the unknown resistance is connected parallel or series from the given values. Then using the formula for corresponding equivalent resistance, find the value of the unknown resistance.

Formulae are as follow:

$\frac{1}{{R}_{eq}}=\frac{1}{R}+\frac{1}{{R}^{\text{'}}}$

Where, R is resistance.

## Step 3: (a) determining the value of the unknown resistance

Let the unknown resistance connected be R’.

From the given values, we can write that ${R}_{eq}

This implies that the unknown resistance is connected in parallel.

Hence,

$\frac{1}{{R}_{eq}}=\frac{1}{R}+\frac{1}{{R}^{\text{'}}}\phantom{\rule{0ex}{0ex}}\therefore {R}_{eq}=\frac{R{R}^{\text{'}}}{R+{R}^{\text{'}}}\phantom{\rule{0ex}{0ex}}3=\frac{12{R}^{\text{'}}}{12+{R}^{\text{'}}}\phantom{\rule{0ex}{0ex}}36+3R\text{'}=12R\text{'}\phantom{\rule{0ex}{0ex}}{R}^{\text{'}}=4.00\text{Ω}$

Hence, the value of the unknown resistance is ${R}^{\text{'}}=4.00\text{Ω}$

## Step 3: (a) Determining the unknown resistance should be connected in series or in parallel

From part a),

it can be concluded that the unknown resistance should be connected in parallel.

Hence, the unknown resistance should be connected in parallel.

Therefore, by using the formula for corresponding equivalent resistance, unknown resistance can be determined.