JEE MAIN - Physics (2022 - 26th July Morning Shift - No. 23)
Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length $$l_{1}$$ is $$40 \mathrm{~cm}$$. Now an unknown resistance $$x$$ is connected in series with $$\mathrm{P}$$ and new balancing length is found to be $$80 \mathrm{~cm}$$ measured from the same end. Then the value of $$x$$ will be ____________ $$\Omega$$.
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Answer
20
Explanation
$${P \over {40}} = {Q \over {60}}$$ ...... (1)
$${{P + x} \over {80}} = {Q \over {20}}$$ ..... (2)
$${P \over {P + x}} \times {{80} \over {40}} = {{20} \over {60}}$$
$${4 \over {4 + x}} \times 2 = {1 \over 3}$$
$$24 = 4 + x$$
$$x = 20$$
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