Two wires $A$ and $B$ with circular cross sections are made of the same metal and have equal lengths, but the resistance of wire A is three times greater than that of wire B. What is the ratio of the cross sectional area of $A$ to that of $B$ ?

3

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\sqrt{3}

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1

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1 / \sqrt{3}

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\frac{1}{3}

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Solution

The correct option is E $\frac{1}{3}$
Given,
Lenght of both wire is $l_{A} = l_{B} = l$
Resistivity of both wire is $ρ_{A} = ρ_{b} = ρ$
Resistance of A, $R_{A} = 3 R_{B}$ (Where, $R_{B}$ Resistance of B)

Now,
$∵ R = ρ \frac{l}{A}$

Fro above equation, $ρ_{A} \frac{l_{A}}{A_{A}} = 3 ρ_{B} \frac{l_{B}}{A_{B}}$

$ρ \frac{l}{A_{A}} = 3 ρ \frac{l}{A_{B}}$

$\frac{A_{A}}{A_{B}} = \frac{1}{3}$

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Similar questions

Two wires A and B are of equal lengths,different are of cross-section and made up of same material

(i) Name of the property which is same for both the wires

(ii) Name the property which is different for both the wire

(iii) If the resistance of wire A is 4 times the resistance of wire B ,calculate

(A)the ratio of the area of the cross-section

(B)the ratio of the radii of the wires

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