Chapter 27: Q. 67 (page 765)

A $20$ -cm-long hollow nichrome tube of inner diameter $2.8 mm$ , outer diameter $3.0 mm$ is connected, at its ends, to a $3.0 V$ battery. What is the current in the tube?

Short Answer

Expert verified

The current in the tube is $I = 36 A .$

Step by step solution

Given information

Nichrome tube length $= 20 c m$

Nichrome tube inner diameter $= 2.8 m m$

Nichrome tube outer diameter $= 3.0 m m$

Voltage $= 3.0 V$

Explanation

Use the $I = \frac{V}{R} \to (1)$ formula,

The area of the tube is provided by the area of the outer circle $D = 3.0 mm$ minus the area of the inner circle $d = 2.8 mm$ :

$A = (0 . 003^{2} \times π - 0 . 0028^{2} \times π)$

role="math" localid="1649165023302" $A = 3.64 \times 10^{- 6} m^{2}$

Find the resistance of this tube,

$R = \frac{(ρ \times L)}{A}$

Where $L$ is the length of the wire and $A$ is the outer area minus the inner area and rho is the resistivity of nichrome.

role="math" localid="1649165124828" $R = [\frac{(1.5 Ω m \times 10^{- 6} \times 0.02 m)}{3.64 \times 10^{- 6} m^{2}}]$

$R = 0.0823 Ω$

Substitute the value in equation (1)

$I = \frac{3 V}{0.0823 Ω}$

$I = 36.44 A$

Final Answer

Hence, the current in the tube is $36 A .$

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A $20$ -cm-long hollow nichrome tube of inner diameter $2.8 mm$ , outer diameter $3.0 mm$ is connected, at its ends, to a $3.0 V$ battery. What is the current in the tube?

Short Answer

Step by step solution

Given information

Explanation

Final Answer

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A20-cm-long hollow nichrome tube of inner diameter 2.8mm, outer diameter3.0mmis connected, at its ends, to a 3.0Vbattery. What is the current in the tube?

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

Electric Charge Field and Potential

Conservation of Energy and Momentum

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Electrostatics

Study anywhere. Anytime. Across all devices.

A $20$ -cm-long hollow nichrome tube of inner diameter $2.8 mm$ , outer diameter $3.0 mm$ is connected, at its ends, to a $3.0 V$ battery. What is the current in the tube?