blessingchada07
contestada

Some copper wire has a resistance of 200 ohms at 20 degrees C . A current is then passed through the same wire and the temperature rises to 90 degrees C. Determine the resistance of the wire at 90 degrees correct to the nearest ohm assuming the coefficient of resistance is 0.004/degree C at 0 degrees ​

Respuesta :

asuwafohjames

Answer:

256 ohms

Explanation:

Applying,

R = R'[1+α(T-T')]............. Equation 1

Where R = Final resistance of the wire, R' = Initial resistance of the wire, T = Final temperature, T' = Initial temperature, α = Temperature coefficient of resistance

From the question,

Given: R' = 200 ohms, T = 90 degrees, T' = 20 degrees, α = 0.004/degree

Substitute these values into equation 1

R = 200[1+0.004(90-20)]

R = 200[1+0.28]

R = 200(1.28)

R = 256 ohms

Eduard22sly

The resistance of the wire at 90 °C correct to the nearest ohm assuming the coefficient of resistance is 0.004 °C¯¹ is 256 ohm

Data obtained from the question

  • Original resistance (R₁) = 200 ohm
  • Original temperature (T₁) = 20 °C
  • Coefficient of resistivity (α) = 0.004 °C¯¹
  • New temperature (T₂) = 90 °C
  • New resistance (R₂) =?

How to determine the new resistance

α = R₂ – R₁ / R₁(T₂ – T₁)

0.004 = R₂ – 200 / 200(90 – 20)

0.004 = R₂ – 200 / 200(70)

0.004 = R₂ – 200 / 14000

Cross multiply

R₂ – 200 = 0.004 × 14000

R₂ – 200 = 56

Collect like terms

R₂ = 56 + 200

R₂ = 256 ohm

Learn more about linear expansion:

https://brainly.com/question/23207743

Otras preguntas