First slide

Temperature dependence

Question

30. The resistance of iron wire is $10 Ω$ and $α = 5 \times 10^{- 3} /^{0} C$ . If a current of 30A is flowing in it at $20^{0} C$ , keeping the potential difference across its length constant, if the temperature is increased to $120^{0} C$ , what is the current flowing through that wire?

Easy

A

10A
B

20A
C

15A
D

25A

Solution

$α = \frac{R_{2} - R_{1}}{R_{1} t_{2} - R_{2} t_{1}}$
$o r, R_{2} = R_{1} (1 + α t) (a p p r o x i m a t e l y)$
$R_{2} = 10 (1 + 5 \times 10^{- 3} \times 100)$
$= 10 (1 + 0.5)$
$= 15 Ω$
$i_{1} R_{1} = i_{2} R_{2}$
$10 \times 30 = i_{2} (15)$
$i_{2} = 20 A$

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