the resistance of a silver wire at 0°C is 1.25ohm. Up to what temperature it must be heated so that its resistance is doubled?The temperature coeffecient of resistance of silver is 0.00375°C.Will the tenperature be the same fir all conductors of silver?
Answers
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The resistance of a silver wire at 0°C is 1.25Ω, the temperature coefficient of resistance of sliver is 0.0375°C.
We have to find the temperature of it so that its resistance is doubled.
resistance and temperature relation :
resistance depends on the temperature of a conductor, change in the length of the temperature is directly proportional to the change in the temperatureand initial resistance of the conductor. it is observed that the increasing the temperature , increase the resistance of conductor.
i.e., ΔR ∝ R₀ΔT
⇒ ΔR = R₀αΔT , here α is temperature coefficient of resistance.
⇒ R - R₀ =R₀αΔT
⇒ R = R₀(1 + αΔT)
here, R₀ = initial resistance = 1.25Ω
α = temperature coefficient = 0.00375°C
and R = 2R₀
∴ 2R₀ = R₀[1 + 0.00375 × (T - 0)]
⇒ 2 = 1 + 0.00375 × T
⇒ T = 1/0.00375 = 266.67°C
Therefore the final temperature of the silver wire is 266.67°C
Will the temperature be the same for all conductors of silver for all the shapes ?
yes, of course, change in resistance doesn't depend on the shape and size of the material. it just depend on the temperature coefficient of it which is material property. it is same for the same material. for all conductors of silver, temperature coefficient must be same.