A copper wire has radius 0.800 mm and carries current I at 20.0°C. A silver wire with radius 0.500 mm carries the same current and is also at 20.0°C. Let Ecu be the electric field in the copper wire and Eag be the electric field in the silver wire. Use the resistivities at room temperature for copper. PCu = 1.72 x 10^-8. m and for silver PAE = 1.47 x 10^-8. m. What is the ratio Ecu/Eng?

Question

Physics

Rambo

19 April, 10:45

A copper wire has radius 0.800 mm and carries current I at 20.0°C. A silver wire with radius 0.500 mm carries the same current and is also at 20.0°C. Let Ecu be the electric field in the copper wire and Eag be the electric field in the silver wire. Use the resistivities at room temperature for copper. PCu = 1.72 x 10^-8. m and for silver PAE = 1.47 x 10^-8. m. What is the ratio Ecu/Eng?

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Answers (1)

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Gabrielle · Answer 1

Ecu/Eag = 0.46

Explanation:

E = PI/A

Ecu = Pcu * I/A

Pcu = 1.72*10^-8 ohm-meter

r = 0.8 mm = 0.8/1000 = 8*10^-4 m

A = πr^2 = π * (8*10^-4) ^2 = 6.4*10^-7π

Ecu = 1.72*10^-8I/6.4*10^-7π = 0.026875I/1

Eag = Pag * I/A

Pag = 1.47*10^-8 ohm-meter

r = 0.5 mm = 0.5/1000 = 5*10^-4 m

A = πr^2 = π * (5*10^-4) ^2 = 2.5*10^-7π

Eag = 1.47*10^-8I/2.5*10^-7π = 0.0588I/π

Ecu/Eag = 0.026875I/π * π/0.0588I = 0.46