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Standard XII

Physics

Kirchoff's Voltage Law

Four resistan...

Question

Four resistances of $15 Ω, 12 Ω, 4 Ω$ and $10 Ω$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of $10 Ω$ to balance the network is _____ $Ω$ .

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Solution

The Wheatstone bridge balance condition is given by,
$\frac{P}{Q} = \frac{S}{R}$
Let resistance $R^{'}$ is connected in parallel with resistance $S$ of $10 Ω$
$∴ \frac{15}{12} = \frac{(\frac{10 R^{'}}{10 + R^{'}})}{4}$
$\Rightarrow 10 + R^{'} = 2 R^{'}$
$∴ R^{'} = 10 Ω$
Hence, $10$ is the correct answer.

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Four resistances of 15 Ω,12 Ω,4 Ω and 10 Ω respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10 Ω to balance the network is _____ Ω.

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Four resistances of $15 Ω, 12 Ω, 4 Ω$ and $10 Ω$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of $10 Ω$ to balance the network is _____ $Ω$ .