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Chapter 26: Q72P (page 770)

A steel trolley-car rail has a cross-sectional area of56.0cm2. What is the resistance of 10.0 kmof rail? The resistivity of the steel is3.00×10-7Ωm.

Short Answer

Expert verified

The resistance of 10km rail is 0.536Ω.

Step by step solution

01

The given data

a) Cross-sectional area,A=56.0×10-4m2

b) Resistivity,ρ=3.00×10-7Ω.m

c) The length of the rail,L=10.0×103m

02

Understanding the concept of the resistance

If a steel trolley car rail moves with its speed having a particular cross-section area, we can find the resistance of that rail by considering the formula for resistance R= ρL/A, where, is the resistivity of the steel and L is the distance traveled by rail and A is its cross-sectional area.

Formulae:

The resistance value of a material, R=ρLA (i)

03

Calculation of the resistance

Using the given data in equation (i), we can get the value of the resistance of the rail as follows:

R=3.00×10710×10356.0×10-4=0.536Ω

Hence, the value of the resistance is 0.536Ω.

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Most popular questions from this chapter

Figure 26-15 shows cross sections through three long conductors of the same length and material, with square cross sections of edge lengths as shown. Conductor Bfits snugly within conductor A, and conductor Cfits snugly within conductor B. Rank the following according to their end-to-end resistances, greatest first: the individual conductors and the combinations of A+B(Binside A),B+C(Cinside B), and A+B+C(Binside Ainside C).

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