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Chapter 28: Q. 44 (page 792)

A $2.0 m$ long, $1 mm$ diameter wire has a variable resistivity given by
localid="1649324855366" $蚁 (x) = (2.5 脳 10^{- 6}) [1 + {(\frac{x}{1.0})}^{2}] 鈩� m$
where x is measured from one end of the wire. What is the current if this wire is connected to the terminals of a $9.0 V$ battery?

Short Answer

Expert verified

The current in the wire will be $0.6 A .$

Step by step solution

01

Given information

We have given

Length of the wire = $2 m$

Diameter of the wire = $1 mm$

Resistivity $蚁 (x) = (2.5 脳 10^{- 6}) [1 + {(\frac{x}{1.0})}^{2}] 鈩� m$

Voltage = $9 V$

We have to find the current in the wire.

02

Simplify

We know the resistance

$R = 蚁 \frac{L}{A}$

where area will be

$A = 蟺 \frac{D^{2}}{4} = 蟺 \frac{10^{- 6}}{4} = 7.85 脳 10^{- 7} m^{2}$

We can see here the length is $2 m .$

So x can change from $0 to 2 .$

Then

localid="1649325644831" $R = \frac{1}{A} {鈭�}_{0}^{2} 蚁 (x) dx R = \frac{1}{7.85 脳 10^{- 7}} {鈭�}_{0}^{2} (2.5 脳 10^{- 6}) [1 + {(\frac{x}{1.0})}^{2}] dx R = 0.318 {[x + \frac{x^{3}}{3}]}_{0}^{2} R = 15 鈩�$

Then current will be

$I = \frac{V}{R} = \frac{9}{15} I = 0.6 A$

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Most popular questions from this chapter

The 10 鈩� resistor in FIGURE EX28.29 is dissipating $40 W$ of power. How much power are the other two resistors dissipating?

The five identical bulbs in FIGURE $E X 28.11$ are all glowing. The battery is ideal. What is the order of brightness of the bulbs, from brightest to dimmest? Some may be equal.

A. $P = T > Q = R = S$

B. $P > Q = R = S > T$

C. $P = T > Q > R = S$

D. $P > Q > T > R = S$

A 50 mF capacitor that had been charged to 30 V is dis-charged through a resistor. FIG颅URE P28.70 shows the capacitor voltage as a function of time. What is the value of the resistance?

The circuit of FIGURE has two resistors, with $R_{1} > R_{2}$ . Which of the two resistors dissipates the larger amount of power? Explain.

What is the equivalent resistance between points a and b in FIGURE EX28.27?

See all solutions

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