Wire Resistance Calculator:
Enter the values of material’s resistivity, ρ(Ω.m), wire’s length, L(m) and cross-sectional area, A(m2) to determine the value of Resistance, R(Ω).
Wire Resistance Formula:
Wire resistance is the opposition that a wire offers to the flow of electric current through it. This resistance is a result of the wire’s material, length, cross-sectional area, and the inherent resistivity of the material. A wire with a higher resistivity or longer length has greater resistance, whereas increasing the cross-sectional area decreases resistance.
The resistivity is a property specific to the material, expressed in ohm-metres.The resistance of a wire is important in electrical and electronic systems because it affects the efficiency of current flow, power loss, and heating of the wire.
The relationship between resistance, resistivity, length, and cross-sectional area can be expressed mathematically using the formula R(Ω) = ρ(Ω.m) * (L(m) / A(m2)), where R is the resistance in ohms, ρ is the material resistivity in ohm-metres, L is the length of the wire in metres and A is the cross-sectional area in square metres.
Resistance, R(Ω) in Ohms of a wire is equal to the product of its material’s resistivity, ρ(Ω.m) in Ohm metres and the wire’s length, L(m) in metres divided by its cross-sectional area, A(m2) in square metres.
Resistance, R(Ω) = ρ(Ω.m) * (L(m) / A(m2))
R(Ω) = resistance in Ohms, Ω.
ρ(Ω.m) = material’s resistivity in Ohms metres, Ω.m.
L(m) = length in metres, m.
A(m2) = area in square metres, m.
Wire Resistance Calculation:
1.A copper wire has a length of 100 metres and a cross-sectional area of 0.0001 square metres. The resistivity of copper is 1.68 * 10−8 ohm-metres. Calculate the resistance of the wire.
Given: ρ(Ω.m) = 1.68 * 10−8 Ω.m, L(m) = 100m, A(m2) = 0.0001m2.
Resistance, R(Ω) = ρ(Ω.m) * (L(m) / A(m2))
R(Ω) = 1.68 * 10−8 Ω * (100 / 0.0001)
R(Ω) = 1.68 * 10−8 Ω * 1000000
R(Ω) = 0.0168 Ω.
2.A wire has a resistance of 0.5 ohms, a cross-sectional area of 0.00005 square metres, and the resistivity of its material is 2.5 * 10−7 ohm-metres. Find the length of the wire.
Given: ρ(Ω.m) = 2.5 * 10−7 Ω.m, R(Ω) = 0.5 Ω, A(m2) = 0.00005m2.
Resistance, R(Ω) = ρ(Ω.m) * (L(m) / A(m2))
L(m) = R(Ω) * A(m2) / ρ(Ω.m)
L(m) = 0.5 * 0.00005 / 2.5 * 10−7
L(m) = 0.000025 / 2.5 * 10−7
L(m) = 100m.