Household wiring uses copper wire with a 1.5 Times 10^-13 m^2 cross sectional ar

Question

Household wiring uses copper wire with a 1.5 Times 10^-13 m^2 cross sectional area. Find the resistance of a 1610 m length of this wire at 20 degree C. The resistivity of cooper wire at 20 degree C is 1.72 Times 10^-8 Ohm middot m. Find the resistance of this wire if its temperature is raised to 150 degree C. The temperature coefficient of resistance of copper is 0.00393 (degree C)^-1. A current flows through a typical automobile headlight. How many coulombs of charge will flow through the headlight during a nonstop 2.5 hour nighttime drive? (3600 s = 1 hour) A steady current of 48 A flows through a long aluminum conductor with cross sectional area 1.6 Times 10^-3 m^2. The resistivity of aluminum is 2.75 Times10^-8 Ohm middot m. For a 50 m section of this conductor find: current density, resistance per meter electric field within the conductor, and potential drop across this section.

Explanation / Answer

1 ans

(a)ans

area A=1.5*10^-5 m^2

length L=1610 m

resistivity p=1.72*10^-8 ohm-m

now we find the resistance

resistance R=pL/A=1.72*10^-8*1610/1.5*10^-5=1.846 ohms

(b)ans

the resistance R=1.846[1+0.00393(150-20)]=2.79 ohms

3 ans

current I=48 A

area of cross sectional A=1.6*10^-3 m^2

length L=50 m

resistivity p=2.75*10^-8 ohm-m

(a) current density J=i/A=48/1.6*10^-3=3*10^4 A/m^2

(b) resistance R=pL/A=2.75*10^-8*50/1.6*10^-3=8.6*10^-4 ohms

(c) electric field E=pJ=2.75*10^-8*3*10^4=8.3*10^-4 N/m

(d) the potential differeence V=iR=48*8.6*10^-4=0.04128 V

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