Question

Find the temperature at which the resistance of a conductor increases by 25% of its value at 27°C. The temperature coefficient of resistance of the conductor is 2.0 × 10⁻⁴°C⁻¹.

Answer 1

Given, temperature coefficient, α = 2.0 × 10⁻⁴°C⁻¹

R₂₇ = R(say), `R_T = R + 25/100R = 1.25R`    ...(i)

T₁ = 27 + 273 = 300 K

α = 2.0 × 10⁻⁴°C⁻¹

From relation,

R_T = R₂₇ [1 + α (T₂ − 300)]   ...(ii)

1.25 R = R[1 + 2.0 × 10⁻⁴(T₂ − 300)]

1 + 2.0 × 10⁻⁴ (T₂ − 300) = 1.25

or 2.0 × 10⁻⁴ (T₂ − 300) = 0.25

`T_2 - 300 = 0.25/(2.0 xx 10^-4)`

= `(0.25 xx 10^4)/2`

= 1250

T₂ = 1250 + 300

T₂ = 1550 K