a wire having a mass if 1kg possess a resistance of 0.1 ohm . of the resistivity of material of wire is 10^-7ohm meter and density of material of wire is 10^4kg/m^3, then length of wire is
Answers
GIVEN
Mass of the wire = 1 kg
Resistance = 0.1 ohm
Resistivity of the wire = 10^-7
Density of the material = 10⁴ kg/m³
TO FIND
Length of the wire.
SOLUTION
Volume = m/d =1/ 10⁴ = 10^-4 m³
Where m = mass of wire
d = density
Volume = A*l = 10⁴
Where A = area
l = length of wire
Resistance = pl/A
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
Given info : a wire having a mass if 1 kg possess a resistance of 0.1 ohm . of the resistivity of material of wire is 10^-7ohm meter and density of material of wire is 10⁴ kg/m³.
To find : The length of wire is .....
solution : mass of the wire, m = 1 kg
density of the wire , d = 10⁴ kg/m³
so the volume of the wire , V = m/d = 1/10⁴ = 10¯⁴ m³ .......(1)
we know, R = ρl/A
⇒R = ρl²/Al
⇒R = ρl²/V
where R is resistance of wire, l is length of wire and A is cross sectional area of the wire.
here, R = 0.1 Ω
ρ = 10^-7 Ω m
V = 10¯⁴ m³
so, 0.1 = 10^-7 × l²/10¯⁴
⇒100 = l²
⇒l = 10 m
Therefore the length of the wire is 10m.
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