The temperature coefficient of resistivity for the metal gold is 0.0034 (C )1, and for tungsten it is 0.0045 (C )1. The resistance of a gold wire increases by 7.0% due to an increase in temperature. For the same increase in temperature, what is the percentage increase in the resistance of a tungsten wire

% increase in resistance of tungsten = 9.27%

Explanation:

We are given:

Co-efficient of resistivity for the metal gold; α_g = 0.0034 /°C

Co-efficient of resistivity for tungsten;α_t = 0.0045 /°C

% Resistance change of gold wire due to temperature change = 7%

Now, let R1 and R2 be the resistance before and after the temperature change respectively.

Thus;

(R2 - R1)/R1) x 100 = 7

So,

(R2 - R1) = 0.07R1

R2 = R1 + 0.07R1

R2 = 1.07R1

The equation to get the change in temperature is given as;

R2 = R1(1 + αΔt)

So, for gold,

1.07R1 = R1(1 + 0.0034*Δt)

R1 will cancel out to give;

1.07 = 1 + 0.0034Δt

(1.07 - 1)/0.0034 = Δt

Δt = 20.59°C

For this same temperature for tungsten, let Rt1 and Rt2 be the resistance before and after the temperature change respectively and we have;

Rt2 = Rt1(1 + α_t*Δt)

So, Rt2/Rt1 = 1 + 0.0045*20.59

Rt2/Rt1 = 1.0927

From earlier, we saw that;

(R2 - R1)/R1) x 100 = change in resistance

Similarly,

(Rt2 - Rt1)/Rt1) x 100 = change in resistance

Simplifying it, we have;

[(Rt2/Rt1) - 1] × 100 = %change in resistance

Plugging in the value of 1.0927 for Rt2/Rt1, we have;

(1.0927 - 1) × 100 = %change in resistance

%change in resistance = 9.27%

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