Two rods of length $ℓ$ and $2 ℓ$ thermal conductivities $2 K$ and $K$ are connected end to end. If cross sectional areas of two rods are equal, then equivalent thermal conductivity of the system is

(6 / 5) K

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1.5 K

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1.2 K

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(8 / 9) K

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Solution

The correct option is B $(6 / 5) K$
In series, $R (e f f) = R 1 + R 2$
$R = \frac{l}{K A}$
$R (e f f) = \frac{l}{2 K A} + \frac{2 l}{K A}$
$\frac{3 l}{K e f f} = \frac{5 l}{2 K A}$
$K e f f = \frac{6 K}{5}$

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