Chapter 21: Q62PE (page 777)

Suppose you want to measure resistances in the range from $10.0 Ω$ to $10.0 kΩ$ using a Wheatstone bridge that has $\frac{R_{2}}{R_{1}} = 2.000$ . Over what range should $R_{3}$ be adjustable?

Short Answer

Expert verified

The range over which the value $R_{3}$ is adjustable is $R_{3} = 5 Ω - 5 kΩ$ .

Step by step solution

Concept Introduction

A Wheatstone bridge is an electrical circuit that balances two legs of a bridge circuit, one of which includes the unknown component, to measure an unknown electrical resistance. The circuit's main advantage is its capacity to deliver exceedingly exact readings.

Given Information

The value range for the resistance in a Wheatstone bridge: $R_{x} = 10 Ω - 10 kΩ$ .
The value of $\frac{R_{2}}{R_{1}} = 2$ .

Range for resistance

Calculate the necessary resistance $R_{3}$ for the range by calculating $R_{3}$ what corresponds $R_{x} = 10 Ω$ to $R_{x} = 10 Ω$ and using the relation,

$\frac{R_{x}}{R_{3}} = \frac{R_{2}}{R_{1}}$

The calculation for the minimum value –

role="math" localid="1656396469353" $R_{3}^{\min} = R_{3}^{\min} (\frac{R_{1}}{R_{2}}) = 10 Ω \times (\frac{1}{2}) = 5 Ω$

The calculation for the maximum value,

$R_{3}^{\max} = R_{3}^{\max} (\frac{R_{1}}{R_{2}}) = 10 kΩ \times (\frac{1}{2}) = 5 kΩ$

Therefore, the resistance range is $R_{3} = 5 Ω - 5 kΩ$ .

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Suppose you want to measure resistances in the range from $10.0 Ω$ to $10.0 kΩ$ using a Wheatstone bridge that has $\frac{R_{2}}{R_{1}} = 2.000$ . Over what range should $R_{3}$ be adjustable?

Short Answer

Step by step solution

Concept Introduction

Given Information

Range for resistance

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Suppose you want to measure resistances in the range from 10.0Ωto 10.0kΩusing a Wheatstone bridge that has R2R1=2.000. Over what range shouldR3be adjustable?

Short Answer

Step by step solution

Concept Introduction

Given Information

Range for resistance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Electricity and Magnetism

Electric Charge Field and Potential

Work Energy and Power

Mechanics and Materials

Electricity

Study anywhere. Anytime. Across all devices.

Suppose you want to measure resistances in the range from $10.0 Ω$ to $10.0 kΩ$ using a Wheatstone bridge that has $\frac{R_{2}}{R_{1}} = 2.000$ . Over what range should $R_{3}$ be adjustable?