Question

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.30% from its value at 20.0°C. Over what temperature range can it be used (in °C)?

Answer 1

Answer:

- 12.5 °C to 52.5 °C

Explanation:

Let the initial resistance is Ro and the initial temperature is To = 20°C.

temperature coefficient of resistance, α = 0.0004 /°C

Case I : For maximum resistance:

Maximum resistance, R' = Ro + 1.30 % of Ro

$R' = R_{0}\left ( 1+\frac{1.3}{100} \right )=1.013 R_{0}$

let the temperature difference is ΔT.

R' = Ro (1 + αΔT)

1.013 Ro = Ro ( 1 + 0.0004 ΔT)

ΔT = 32.5 °C

So, the maximum value of resistance is

T = 32.5 + 20 = 52.5 °C

Case II: For minimum value of resistance :

Minimum resistance, R'' = Ro - 1.30 % of Ro

$R'' = R_{0}\left ( 1-\frac{1.3}{100} \right )=0.987 R_{0}$

let the temperature difference is ΔT.

R'' = Ro (1 + αΔT')

0.987 Ro = Ro ( 1 + 0.0004 ΔT')

ΔT' = - 32.5 °C

So, the maximum value of resistance is

T' = - 32.5 + 20 = - 12.5 °C

So, the range of temperature is - 12.5 °C to 52.5 °C.