The ratio of thermal conductivity of two rods of different material is 4:3. The two rods of same area and same thermal resistance have length in ratio of?

\frac{l_{1}}{l_{2}} = \frac{4}{3}

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\frac{l_{1}}{l_{2}} = \frac{2}{4}

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\frac{l_{1}}{l_{2}} = \frac{3}{4}

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\frac{l_{1}}{l_{2}} = \frac{5}{4}

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Solution

The correct option is A $\frac{l_{1}}{l_{2}} = \frac{4}{3}$
We know that,

$R_{1} = \frac{ρ_{1}}{k_{1} \times l_{1}} . . . . (I)$

$R_{2} = \frac{ρ_{2}}{k_{2} \times l_{2}} . . . . . (I I)$

Now, according to question

$R_{1} = R_{2}$

$\frac{l_{1}}{k_{1} \times A_{1}} = \frac{l_{2}}{k_{2} \times A_{2}}$

$\frac{l_{1}}{k_{1}} = \frac{l_{2}}{k_{2}}$

$\frac{l_{1}}{l_{2}} = \frac{k_{1}}{k_{2}}$

$\frac{l_{1}}{l_{2}} = \frac{4}{3}$

Hence, this is the required solution

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The ratio of thermal conductivity of two rods of different material is 4:3. The two rods of same area and same thermal resistance have length in ratio of?

The correct option is A l1l2=43We know that, R1=ρ1k1×l1....(I) R2=ρ2k2×l2.....(II) Now, according to question R1=R2 l1k1×A1=l2k2×A2 l1k1=l2k2 l1l2=k1k2 l1l2=43 Hence, this is the required solution