First slide

Temperature dependence

Question

The resistance of a conductor is 5 ohm at 50⁰C and 6 ohm at 100⁰C. Its resistance at 0⁰C is

Easy

A

1 ohm
B

2 ohm
C

3 ohm
D

4 ohm

Solution

$\begin{array}{l} \frac{R_{1}}{R_{2}} = \frac{(1 + α t_{1})}{(1 + α t_{2})} \Rightarrow \frac{5}{6} = \frac{(1 + α \times 50)}{(1 + α \times 100)} \Rightarrow α = \frac{1}{200} p e r^{0} C \\ A g a i n b y R_{t} = R_{0} (1 + α t) \\ \Rightarrow 5 = R_{0} (1 + \frac{1}{200} \times 50) \Rightarrow R_{0} = 4 Ω \end{array}$

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