In the circuit shown in the diagram below, two thick wires connect a 1.7 volt ba
ID: 2141091 • Letter: I
Question
In the circuit shown in the diagram below, two thick wires connect a 1.7 volt battery to a Nichrome (NiCr) wire. Each thick connecting wire is 16 cm long, and has a radius of 11 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 8 cm long, and has a radius of 3 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
In the circuit shown in the diagram below, two thick wires connect a 1.7 volt battery to a Nichrome (NiCr) wire. Each thick connecting wire is 16 cm long, and has a radius of 11 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 8 cm long, and has a radius of 3 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/mExplanation / Answer
Total length of copper wire Lc = 2 * 16 cm
= 0.32 m
radius of copper wire rc = 11mm
=1.1* 10-2 m
Hence resistance of copper wire RC = ?C * Lc / ? * rc2
= 1.68 * 10-8 * 0.32 / 3.14 * (1.1*10-2)2
= 1.4132* 10-5 ?
here ?C = resistivity of copper = 1.68 * 10-8 ? - m
Total length of nichrome wire Ln = 8 cm
= 0.08 m
radius of nichrome wire rn = 3 mm
= 3 * 10-3 m
Hence resistance of nichrome wire Rn = ?n * Ln / ? * rn2
= 1.10 10-6 * 0.08 / 3.14 * (3 * 10-3)2
= 3.1139* 10-3 ?
here ?n = resistivity of nichrome = 1.10 * 10-6 ? - m
Net resistance R = Rc + Rn
= 1.4132* 10-5 + 3.1139* 10-3
= 3.1280 * 10-3 ?
Current I = V / R
= 1.7/ 3.128* 10-3
= 0.5434 * 103 A
If n be electron concentration, e charge of electron, ? be electron mobility, then
electric field inside wire E = V / L = I * R / L
a. For copper EL = I * Rc / Lc
= 0.543 * 103 * 1.4132 * 10-5 / 0.32
= 2.398 * 10-2 V/m
b. For nichrome En = I * Rn / Ln
= 0.543 * 103 *3.1139* 10-3 / 0.08
= 21.13559625 V/m