a wire having a mass of 1 kg possesss a resistance of 0.1ohm. if the resistivity of material of wire is 10^-7 and density of a material of wire is 10⁴ kg/m³. The legth of wire is
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Answers
Given : R=2Ω l=1 m d=0.4 mm =0.0004 m
Cross section area of wire A=
4
πd
2
=
4
π×(0.0004)
2
=1.256×10
−7
m
2
Resistivity of the material ρ=
l
RA
∴ ρ=
1
2×1.256×10
−7
=2.514×10
−7
Ωm
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The correct question is:
A wire having a mass of 1kg possess a resistance of 0.1 ohm. if the resistivity of material of wire is 10^-7 ohm m and density of material of wire is 10^4 kg/m^3, then the length of the wire is?
Given:
Mass of the wire = 1 kg
Resistance = 0.1 ohm
Resistivity of the wire = 10^-7
Density of the material = 10^4 kg/m³
To find:
Length of the wire.
Solution:
Volume = m/d =1/ 10^4 = 10^-4 m³
Where m = mass of wire
d = density
Volume = A*l = 10^-4 m³
Where A = area
l = length of wire
Resistance = pl/A ohms
Where p = resistivity
l = length of wire
A = area of wire
0.1 = 10^-7 * l/ A
Since A = 10^-4/l, Putting the value of A we get:
0.1 = 10^-7 * l²/ 10^-4
100 = I²
l = 10 m