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An aluminium $(α_{A l} = 4 \times 10^{- 3} l^{ο} C)$ wire resistance $' R_{1}'$ and carbon wire $(α_{c} = 0.5 \times 10^{- 3} l^{ο} C)$ resistance $' R_{2}'$ are connected in series to have a resultant resistance of 18 ohm at all temperatures. The values of $R_{1} a n d R_{2}$ in ohms

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14, 4

13, 5

2, 16

12 , 6

answer is A.

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Detailed Solution

$α_{A l} = 4 \times 10^{- 3} \Rightarrow R_{1}$

$α_{C} = 0.5 \times 10^{- 3} \Rightarrow R_{2}$

$α_{A l} R_{1} = α_{C} R_{2}$

$4 \times 10^{- 3} R_{1} = 0.5 \times 10^{- 3} R_{2}$

$R_{2} = 8 R_{1}$

$R_{1} + R_{2} = 18 Ω$

$R_{1} = 2 Ω; R_{2} = 16 Ω$

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