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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

01

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 $= 3.0 V$

02

Explanation

Use the $I = \frac{V}{R} 鈫� (1)$ 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 $d = 2.8 mm$ :

$A = (0 . 003^{2} 脳蟺 - 0 . 0028^{2} 脳蟺)$

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

Find the resistance of this tube,

$R = \frac{(蚁脳 L)}{A}$

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" $R = [\frac{(1.5 惟 m 脳 10^{- 6} 脳 0.02 m)}{3.64 脳 10^{- 6} m^{2}}]$

$R = 0.0823 惟$

Substitute the value in equation (1)

$I = \frac{3 V}{0.0823 惟}$

$I = 36.44 A$

03

Final Answer

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

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Most popular questions from this chapter

The total amount of charge in coulombs that has entered a wire at time $t$ is given by the expression localid="1648639892228" $Q = 4 t - t^{2}$ , where $t$ is in seconds and $t 鈮� 0$ .
a. Find an expression for the current in the wire at time $t$ .
b. Graph $I$ versus $t$ for the interval $0 鈮� t 鈮� 4 s$ .

For what electric field strength would the current in a $2.0 m m$ diameter nichrome wire be the same as the current in a $1.0 m m$ diameter aluminum wire in which the electric field strength is $0.0080 V / m$ ?

The starter motor of a car engine draws a current of $150 A$ from the battery. The copper wire to the motor is $5.0 mm$ in diameter and $1.2 m$ long. The starter motor runs for $0.80 s$ until the car engine starts.

a. How much charge passes through the starter motor?

b. How far does an electron travel along the wire while the starter motor is on?

76. A thin metal cylinder of length $L$ and radius $R_{1}$ is coaxial with a thin metal cylinder of length $L$ and a larger radius $R_{2}$ . The space between the two coaxial cylinders is filled with a material that has resistivity $蚁$ . The two cylinders are connected to the terminals of a battery with potential difference $螖 V$ , causing current $I$ to flow radially from the inner cylinder to the outer cylinder. Find an expression for the resistance of this device.

17. What is the mean time between collisions for electrons in (a) an aluminum wire and (b) an iron wire?

See all solutions

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