Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length l₁ is 40 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the value of x will be ________ Ω.

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answer is 20.

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Detailed Solution

$\begin{array}{l} \frac{P}{40} = \frac{Q}{60} . . . . (i) \\ \frac{P + x}{80} = \frac{Q}{20} . . . . . (ii) \\ \frac{P}{P + x} \times \frac{80}{40} = \frac{20}{60} \\ \frac{4}{4 + x} \times 2 = \frac{1}{3} \\ 24 = 4 + x \\ x = 20 \end{array}$

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