Three resistances $R, 2 R$ and $3 R$ of same material and same length have their area of cross-section in the ratio

1 : 2 : 3

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3 : 2 : 1

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6 : 3 : 2

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1 : 2 : 6

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Solution

The correct option is C $6 : 3 : 2$
Resistance of the material $= ρ \frac{1}{A}$ $[ρ =$ resistivity, $l =$ length of the resistor and $A =$ area of cross-section]
Let $R_{1}, R_{2}$ and $R_{3}$ be the three resistances.
$R_{1} = ρ \frac{l}{A_{1}} = R$
$\Rightarrow A_{1} = \frac{ρ l}{R}$
$R_{2} = ρ \frac{1}{A_{2}} = 2 R$
$\Rightarrow A_{2} = \frac{ρ l}{2 R}$
$R_{3} = ρ \frac{1}{A_{3}} = 3 R$
$\Rightarrow A_{3} = \frac{ρ l}{3 R}$
$∴ A_{1} : A_{2} : A_{3} = 6 : 3 : 2$
Hence, the correct answer is option (c).

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