In the circuit shown in the diagram below, two thick wires connect a 1.2 volt ba
ID: 1791197 • Letter: I
Question
In the circuit shown in the diagram below, two thick wires connect a 1.2 volt battery to a Nichrome (NiCr) 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 8.36e+28 mobile electrons per cubic meter, and an electron mobility of 0.00434 (m/s)/(V/m). The Nichrome wire is 7 cm long, and has a radius of 5 mm. Nichrome has 9e+28 mobile electrons per cubic meter, and an electron mobility of 7e-05 (m/s)/(V/m).
What is the magnitude of the electric field in the thick copper wire?
V/m
What is the magnitude of the electric field in the thin Nichrome wire?
V/m
Explanation / Answer
Rc = pcu * (l / A) = 1.68 * 10-8 * 2 * 0.14 / (pi * 0.0092) = 1.85 * 10-5 ohm
RN = pNi * (l / A) = 100 * 10-8 * 0.07 / (pi * 0.0052) = 8.91 * 10-4 ohm
I = V / Rc + RN = (1.2) / (1.85 * 10-5 + 8.91 * 10-4) = 1319 A
JC = I /A = 1319 / (pi * 0.0092) = 5.18 * 106 A/m2
JN = I /A = 1319 / (pi * 0.0052) = 1.68 * 107 A/m2
a) E = JC / n e mu = (5.18 * 106) / (8.36 * 1028 * 1.6 * 10-19 * 0.00434)
= 0.089 V/m
b) E = JN / n e mu = (1.68 * 107) / (9 * 1028 * 1.6 * 10-19 * 7 * 10-5)
= 16.67 V/m