A carbon filament has resistance of 120 $Ω$ at 0^oC what must be the resistance of a copper filament connected in series with carbon so that combination has same resistance at all temperatures.
$\begin{array}{l} α_{carbon} = - 5 \times 10^{- 4} /^{0} C, \\ α_{copper} = 4 \times 10^{- 3} /^{0} C \end{array}$

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120 $Ω$

15 $Ω$

60 $Ω$

210 $Ω$

answer is B.

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Detailed Solution

$\begin{array}{l} R_{1} α_{1} = - R_{2} α_{2} \\ R_{1} (4 \times 10^{- 3}) = 120 \times 5 \times 10^{- 4} \\ R_{1} = \frac{60}{4} = 15 Ω \end{array}$

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