Two wires of same metal have the same length but their cross-sections are in the ratio $3:1$. They are joined in series. The resistance of the thicker wire is $10\,\Omega $. The total resistance of the combination will be ............. $\Omega$
AIPMT 1995,AIIMS 2012, Medium
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For same material and same length
$\frac{{{R_2}}}{{{R_1}}} = \frac{{{A_1}}}{{{A_2}}} = \frac{3}{2}$ $ \Rightarrow $ ${R_2} = 3{R_1}$
Resistance of thick wire ${R_1} = 10\,\Omega $
Resistance of thin wire ${R_2} = 30\,\Omega $
Total resistance in series $ = 10 + 30 = 40\,\Omega$
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