(chapter 18) Answer is provided, provide a step by step solution. In the circuit
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Question
(chapter 18) Answer is provided, provide a step by step solution.
In the circuit shown in the diagram below, two thick wires connecta 1.5 volt battery to a Nichrome (NiCr) wire. Each thick connecting wire is 17 cm long, and has a radius of 10 mm. The thick wires are made of copper, which has 8.36+28 mobile electrons per cubic meter, and an electron mobilty of 0.00434 (ms)Vm). The Nichrome wire is 7 cm long, and has a radius of 2 mm. Nichrome has 9e+28 mobile alectrons per cubic meter, and an electron mobility of 70-05 (m)m). e magnitude of the electric field in the thick copper wire? magnitude of the electric field in the thin Nichrome wire? 367VmExplanation / Answer
Resistance of Copper wire
RCu=pcuLcu/Acu =(1.68*10-8)(2*0.17)/(pi*0.012)=1.818*10-5 ohms
Resistance of nichrome wire
RN=pNLN/AN =(1*10-6)*0.07/(pi*0.0022)=5.57*10-3 ohms
Total Current
I=V/(RCu+RN)=1.5/(1.818*10-5+5.57*10-3)=268.4 A
Current density of copper wire
Jcu=I/Acu =268.4/(pi*0.012)=8.543*105 A/m2
Current density of nichrome wire
JN=I/AN =268.4/(pi*0.0022)=2.136*107A/m2
a)
Electric field in thick copper wire is
Ecu=J/nqu =(8.543*105)/(8.36*1028)(1.6*10-19)(0.00434)
Ecu=0.0147 V/m
b)
Electric field due to nichrome wire is
EN=(2.136*107)/(9*1028)(1.6*10-19)(7*10-5)
EN=21.3 V/m
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