Chapter 27: Q. 34 (page 763)

The resistance of a very fine aluminum wire with a $10 μ m \times 10 μ m$ square cross section is role="math" localid="1649061344586" $1000 Ω$ . A $1000 Ω$ resistor is made by wrapping this wire in a spiral around a $3.0 m m$ diameter glass core. How many turns of wire are needed?

Short Answer

Expert verified

The number of turns of wire are needed is $379$ turns.

Step by step solution

Given Information

Aluminum wire dimension $= 10 μ m \times 10 μ m$

Resistancelocalid="1649061848996" $= 1000 Ω$

Resistor $= 1000 Ω$

Spiral wire diameter $= 3.0 m m$

Explanation

The total length of the wire will be such that

$R = ρ \frac{L}{A} \to (1)$

Express this length as,

$L = \frac{R A}{ρ} = \frac{R a^{2}}{ρ} \to (2)$

where $a$ is the thickness of the wire.

The length fulfills the following condition:

$L = n P$

Where $P = π D$ is the perimeter of the glass core.

The number of turns is therefore,

$n = \frac{L}{P} = \frac{L}{π D}$

Substitute the second expression in the last, finding

localid="1649061681694" $n = \frac{R a^{2}}{ρ π D} = \frac{R a^{2}}{πρD}$

Substitute the expression,

localid="1649062038246" $n = (\frac{1000 Ω \times 0.00001 m^{2}}{π \times 2.8 \times 10^{- 8} Ω m \times 0.003 m})$

$= 379 turns.$

Final Answer

Hence, the number of turns needed are $379$ turns.

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The resistance of a very fine aluminum wire with a $10 μ m \times 10 μ m$ square cross section is role="math" localid="1649061344586" $1000 Ω$ . A $1000 Ω$ resistor is made by wrapping this wire in a spiral around a $3.0 m m$ diameter glass core. How many turns of wire are needed?

Short Answer

Step by step solution

Given Information

Explanation

Final Answer

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The resistance of a very fine aluminum wire with a 10μm×10μm square cross section is role="math" localid="1649061344586" 1000Ω. A 1000Ω resistor is made by wrapping this wire in a spiral around a 3.0mmdiameter glass core. How many turns of wire are needed?

Short Answer

Step by step solution

Given Information

Explanation

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Linear Momentum

Electric Charge Field and Potential

Conservation of Energy and Momentum

Thermodynamics

Physical Quantities And Units

Study anywhere. Anytime. Across all devices.

The resistance of a very fine aluminum wire with a $10 μ m \times 10 μ m$ square cross section is role="math" localid="1649061344586" $1000 Ω$ . A $1000 Ω$ resistor is made by wrapping this wire in a spiral around a $3.0 m m$ diameter glass core. How many turns of wire are needed?