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Estimating Resistance Change of a Resistor/Conductor

Task: Thin Manganin wire of the length l = 0.5 m is glued to the electrically insulating rod. The insulating rod is subsequently stretched by applying axial mechanical force. Prior to stretching the resistance of Manganin wire was R0 = 10 Ω and after applying the axial force R1 = 10.01 Ω.
Determine:
a) diameter of the wire D when no mechanical force is applied;
b) relative length change of the insulating rod Δl / l [%]

Note:
1) Assume no relative movement between the wire and insulating rod;
2) Electrical resistivity change due to stretching can be neglected;
3) Relative deformations in axial and transverse dimensions of the wire are satisfying the Poisson's ratio which is µ=0.35.
4) Electrical resistivity of Manganin is ρ = 43∙10-8 Ωm.

Solution Preview

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Task: Thin Manganin wire of the length l = 0.5 m is glued to the electrically insulating rod. The insulating rod is subsequently stretched by applying axial mechanical force. Prior to stretching the resistance of Manganin wire was R0 = 10 Ω and after applying the axial force R1 = 10.01 Ω.
Determine:
a) diameter of the wire D when no mechanical force is applied;
b) relative length change of the ...

Solution Summary

The solution gives a step-by-step guide on how to estimate resistance change of a metallic resistor/conductor under the influence of axial mechanical force causing stretching. It contains two pages of detailed derivations and calculations with all relevant expressions and formulae.

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