An aluminum αAl=4×10−3/0C wire resistance ‘R1 ’ and carbon wire αC=-0.5×10−3/0C  resistance ‘ R2’ are connected in series to have a resultant resistance of 18 ohm at all temperatures .  The values of  R1 and R2  in ohms

# An aluminum $\left({\mathrm{\alpha }}_{\mathrm{Al}}=4×{10}^{-3}{/}^{0}\mathrm{C}\right)$ wire resistance ‘${\mathrm{R}}_{1}$ ’ and carbon wire $\left({\mathrm{\alpha }}_{\mathrm{C}}=-0.5×{10}^{-3}{/}^{0}\mathrm{C}\right)$  resistance ‘ ${\mathrm{R}}_{2}$’ are connected in series to have a resultant resistance of 18 ohm at all temperatures .  The values of  R1 and R2  in ohms

1. A

2,16

2. B

12,4

3. C

13,5

4. D

14,4

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### Solution:

Given

$\frac{{R}_{1}}{{R}_{2}}=\frac{{\alpha }_{C}}{{\alpha }_{Ai}}=\frac{0.5}{4}=\frac{1}{8}⇒{R}_{2}=8{R}_{1}$

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