Question

A gold wire is originally at 20 ∘C.

Part A

Find the temperature required to raise its resistance by 1 % .

Express your answer with the appropriate units.

Part B

Find the temperature required to raise its resistance by 10 % .

Express your answer with the appropriate units.

Answer 1

Relation of resistance with temperature is given by equation

R=R_ref(1+ α(T-T_ref)

Where R_ref is reference resistance or intial resistance

R resistance after change or final resistance

α temperature coefficient of material

T_ref Reference temperature or intial

T final temperature

Value of temperature coefficient for gold is .0034

(Part a)

1% increase in resistance means if intially it was R than now it is (101/100) R

Substituting in formula we get

1.01R=R(1+.0034(T-20)

T=22.94 degree Celsius

(Part b)

Applying similar concept now increase in resistance is 10%

Let intial resistance be R so now it will be (110/100)R=1.1R

Substituting in formula we get

1.1R=R(1+.0034(T-20))

T=((1.1R/R)-1)/.0034 +20

T=49.41 degree Celsius

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