The temperature of the transformer after the transformer has been in operation for several hours at the given resistance is 21.2 degrees Celsius.
Relationship between resistance and temperature
The relationship between resistance and temperature is given as;
R = R₀( 1 + αΔθ)
From the first resistance, we will have the following equation,
R₁ = R₀( 1 + αΔθ)
50 = R₀(1 + 15α) ------ (1)
From the second resistance, we will have the following equation,
58 = R₀(1 + αT) ------ (2)
Divide (1) by (2)
[tex]\frac{50}{58} = \frac{R_0(1 + 15\alpha)}{R_0(1 + T\alpha)} \\\\\frac{50}{58} = \frac{(1 + 15\alpha)}{(1 + T\alpha)} \\\\50(1 + T\alpha) = 58(1 + 15\alpha)\\\\50 + 50T\alpha = 58 + 870\alpha \\\\50(0.0425)T = (58- 50) + 870(0.0425)\\\\2.125T = 44.975\\\\T = 21.2\ ^0C[/tex]
Thus, the temperature of the transformer after the transformer has been in operation for several hours at the given resistance is 21.2 degrees Celsius.
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