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
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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
Therefore the length of the wire is 10 m.
Given: Mass of the wire = 1 kg
Resistance = 0.1 Ω
Resistivity of the material of wire = 10⁻⁷ Ω-m
Density of the material of wire = 10⁴ kg/m³
To find: Length of the wire.
Solution:
density = mass / Volume
=> Volume = mass/density = 1/ 10⁴ = 10⁻⁴ m³
Volume = cross-section Area x length
10⁻⁴ = A * L
A = cross-section area , L = length of wire
=> A = 10⁻⁴ /L
R = ρL/A
Resistance = R = 0.1 Ω
ρ = resistivity = 10⁻⁷ Ω-m
0.1 = 10⁻⁷ * L/ A
=> 0.1 = 10⁻⁷ * L/ (10⁻⁴ /L)
=> 0.1 = L²/10³
=> 0.1 * 10³ = L²
=> 10² = L²
=> 10 = L
Length of the wire is 10 m.
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