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?

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.