Question

In the circuit shown in the diagram below, two thick wires connect a 1.4 volt battery to a Nichrome (NIC) wire. Each thick connecting wire is 14 cm long, and has a radius of 9 mm. The thick wires are made of copper, which has 8.35+28 mobile electrons per cubic meter, and an electron mobility of 0.00434 (m (V/m). The Nichrome wire is 8 cm long, and has a radius of 4 mm. Nichrome has 9e+28 mobile electrons per cubic meter, and an electron mobility of 7-05 (mus/V/m). What is the magnitude of the electric field in the thick copper wire? VA What is the magnitude of the electric held in the thin Nichrome wire?

Answer 1

1)

Resistance of copper wire,

Rcu = (1.68 x 10^-8 x 2 x 0.14)/(pi x 0.009^2)

Rcu = 1.85 x 10^-5 ohm

Resistance of copper wire,

Rn = (100 x 10^-8 x 0.08)/(pi x 0.004^2)

Rn = 1.59 x 10^-3 ohm

Current, I = 1.4/(Rcu + Rn) = 869.54 A

Current density, J(copper) = 869.54/(pi x 0.009^2)

J_cu = 3.42 x 10^6 A/m^2

J_n = 869.54/(pi x 0.004^2) = 1.78 x 10^7 A/m^2

A)

E = (3.42 x 10^6)/(8.36 x 10^28 x 1.6 x 10^-19 x 0.00434)

E = 0.058 V/m

B)

E = (1.78 x 10^7)/(9 x 10^28 x 1.6 x 10^-19 x 7 x 10^-5)

E = 17.66 V/m

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