First slide

Temperature dependence

Question

The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will be

Moderate

A

4 ohm
B

3 ohm
C

2 ohm
D

1 ohm

Solution

We know that
$R_{t} = R_{0} (1 + αt)$
Applying this formula, we get
$R_{50} = R_{0} (1 + 50 α) = 5 . . . (1)$
and $R_{100} = R_{0} (1 + 100 α) = 6 . . . (2)$
Multiplying eq. (1) by 2, we get
$2 R_{0} (1 + 50 α) = 10$
or $2 R_{0} + 100 α = 10 . . . (3)$
Subtracting eq. (2) from eq.(3), we get
$2 R_{0} - R_{0} = 10 - 6 = 4$
$∴ R_{0} = 4 Ω$

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