Question

A coil of standard annealed copper having a resistance of 50 ohms at 15° is embedded in the core of a large transformer after the transformer has been in operation for several hours the resistance of the material is measured as 58 ohms determine its temperature the temperature coefficient of resistance of the conductor material is 0.04 250 degree celsius at 0 degrees Celsius.
determine its temperature?​

Answer 1

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)

$\frac{50}{58} = \frac{R_0(1 + 15\alpha)}{R_0(1 + T\alpha)} \\\\\frac{50}{58} = \frac{(1 + 15\alpha)}{(1 + T\alpha)} \\\\50(1 + T\alpha) = 58(1 + 15\alpha)\\\\50 + 50T\alpha = 58 + 870\alpha \\\\50(0.0425)T = (58- 50) + 870(0.0425)\\\\2.125T = 44.975\\\\T = 21.2\ ^0C$

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.

Learn more about resistance and temperature here: brainly.com/question/2735534