Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length ${l}_{1}$ is $40cm$ . Now an unknown resistance $x$ is connected in series with $P$ and new balancing length is found to be $80cm$ measured from the same end. Then the value of $x$ will be _____ $Ω$ .

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Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length l _ 1 is 40cm . Now an

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Applying balanced condition for meter bridge
Initially, $\dfrac{P}{Q} = \dfrac{40cm}{60cm} = \dfrac{2}{3} . . . \left(1\right)Finally, \dfrac{P + x}{Q} = \dfrac{80cm}{20cm} = \dfrac{4}{1}$ . . . \left(2\right) $Dividing equation \left(2\right)$ by (\left(1\right) $,$ \dfrac{P + x}{P} = $4 \times$ \dfrac{3}{2} = $6$
$⇒ 1 +$ \dfrac{x}{P} = $6 ⇒$ \dfrac{x}{P} = $5$
$∴ x = 5P = 5 \times 4 = 20Ω$

Resistance are connected in a meter bridge circuit as shown in the...

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