The resistance of a conductor is 10 Ω at 500 C and 15 Ω at 1000 C. Calculate its resistance at 00 C.

The resistance of a conductor is 10 Ω at 50⁰ C and 15 Ω at 100 ⁰ C. Calculate its resistance at 0 ⁰ C.
Solution:

θ_{1}

= 50

^{\circ}

C
resistance at 50

^{\circ}

R_{1}

= 10

Ω

θ_{2}

= 100

^{\circ}

C
resistance at 100

^{\circ}

R_{2}

= 15

Ω

θ

= 0

^{\circ}

resistance at 0

^{\circ}

R

=?
We have,

\begin{aligned} α & = \frac{R_{2} - R_{1}}{R_{1} Δ θ} \\ = \frac{15 - 10}{10 \times 50} \\ = \frac{5}{10 \times 50} \\ = \frac{1}{100} K^{- 1} \end{aligned}

Now,

\begin{aligned} R & = R_{1} (1 + α Δ θ) \\ = 10 (1 + \frac{1}{100} \times (0 - 50)) \\ = 10 (1 - \frac{50}{100}) \\ = 10 \times \frac{1}{2} \\ ∴ R & = 5 Ω \end{aligned}

Hence the resistance at 0

^{\circ}

C is 5

Ω

Physics in Depth