In a circuit two resistances of the same material and cross section area but different lengths $L_{1} a n d L_{2}$ are kept in series. Find the length of the equivalent resistance if it's made of the same material and same cross section area.

L₁ x L₂ / (L₁ +L₂)

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L₁ +L₂

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L₁ - L₂

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1/ L₁ +L₂

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Solution

The correct option is B
L₁ +L₂

Resistance of both the resistance will be $R_{1} = \frac{ρ L_{1}}{A} a n d R_{2} = \frac{ρ L_{2}}{A}$
Since they are in series so R net $R n e t = \frac{ρ L_{n e t}}{A} = R_{1} + R_{2} = \frac{p (L_{1} + L_{2})}{A}$
$S o L_{n e t} = L_{1} + L_{2}$

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