The resistance of a platinum wire at 0°C is 2Ω and 6Ω at 80°C. The temperature coefficient of resistance of the wire is:
(1) 3×10⁻³ °C⁻¹
(2) 0.25 × 10⁻¹ °C⁻¹
(3) 0.25 × 10⁻² °C⁻¹
(4) 0.25 °C⁻¹
Answer (1)
To find the temperature coefficient of resistance ( α ) of the platinum wire, we use the formula:
R t = R 0 ( 1 + α ⋅ t )
Where:
R t is the resistance at temperature t .
R 0 is the resistance at the reference temperature (0°C in this case).
α is the temperature coefficient of resistance.
t is the change in temperature.
Given:
R 0 = 2 Ω at 0°C
R t = 6 Ω at 80°C
t = 80 ° C
Substituting the given values into the formula, we get:
6 = 2 ( 1 + α ⋅ 80 )
First, divide both sides by 2 to simplify the equation:
3 = 1 + 80 α
Subtract 1 from both sides to isolate the 80 α term:
2 = 80 α
Divide both sides by 80 to solve for α :
α = 80 2 = 0.025
Therefore, the temperature coefficient of resistance of the wire is 0.025 ° C − 1 . This corresponds to the third multiple-choice option, (3) 0.25 × 1 0 − 2 \° C − 1 .
