Question

How much would you have to raise the temperature of a copper wire (originally at 20 ?c) to increase its resistance by 18 % ? the temperature coefficient of resistivity of copper is 0.0068 (?c)?1?

Answer 1

The equation for how temperature changes the resistance R is: 

R=R₀(1+α(T-T₀)), where R₀ is the resistance at T₀=20°C, T is the temperature for which we want to calculate the resistance and α is the temperature coefficient for resistance. 

The resistance of the copper wire increases by 18% or by 0.18, so the new value for the resistance is R=1.18*R₀.

T₀=20°C
=0.0068
R=1.18*R₀

Now we need to input that into the equation for resistance change and solve for temperature T.  

1.18R₀=R₀(1+α(T-20)), R₀ cancels out,

1.18=1+α(T-20),

1.18-1=α(T-20), we divide by α,

0.18/α=T-20, we put 20 on the left side,

26.47+20=T

T=46.47°C

So the temperature on which the resistance of copper wire will increase by 18% is T=46.47°C. 

Answer 2

To increase the resistance of the copper wire by 18%, the temperature will be increase to 46.47 °C

Data obtained from the question

• Original temperature (T₁) = 20 °C
• Original resistance (R₁) = R
• New resistance (R₂) = 18% increase = 1.18R
• Coefficient of resistivity (α) = 0.0068 °C¯¹

• New temperature (T₂) =?

How to determine the new temperature

α = R₂ – R₁ / R₁(T₂ – T₁)

0.0068 = 1.18R – R / R(T₂ – 20)

0.0068 = 0.18R / R(T₂ – 20)

0.0068 = 0.18 / (T₂ – 20)

Cross multiply

0.0068 (T₂ – 20) = 0.18

Divide both side by 0.0068

T₂ – 20 = 0.18 / 0.0068

T₂ – 20 = 26.47

Collect like terms

T₂ = 26.47 + 20

T₂ = 46.47 °C

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