Suppose you wish to fabricate a uniform wire from 2.40g of copper. The wire is t

Question

Suppose you wish to fabricate a uniform wire from 2.40g of copper. The wire is to have a resistance of R=0.560 ohm and all the copper is to be used. What must be the length of this wire? What must be the diameter of this wire? A portion of Nichrome wire of radius 3.15 mm is to be used in winding a heating coil. If the coil must draw a current of 0.55 A when a voltage of 120 V is applied across its ends, find the following. (Take the resistivity of nichrome to be 1.50 times 10^-6 Ohm.m.) the required resistance of the coil the length of wire you must use to wind the coil

Explanation / Answer

1)
Resistance of a wire in
R = L/A
is resistivity of the material in -m
L is length in meters
A is cross-sectional area in m²
A = r², r is radius of wire in m
resistivity Cu 17.2e-9 -m

(17.2e-9)L/(r²) = 0.560

volume of the wire is V = r²L
density copper 8960 kg/m³
Volume = 0.00240 kg / 8960 kg/m³ = 2.678571429 e-7m³

so we have AL = r²L = 2.678571429 e-7
and (17.2e-9)L/A = 0.560
two equations in 2 unknowns.
0.560A = (17.2e-9)L
A = 3.071428571 e-8 L
AL = 2.678571429 * 10^-7
(3.071428571 e-8L)L = 2.678571429 e-7

L = 2.953122116 meters

A = 3.071428571 e-8 L

A = 9.070303642 e-8 m²

2)

A) As we know that

R=V/I

R = 120V/9.55A= 12.56544503 ohm

B) R=pl/A

solved for l to get

l=RA/p

l = 12.56544503 ohm*pi*(3.15*10^-3m)^2/1.5 *10^-6ohm*m^2 to get

l = 261.1304972 m

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