Question

Plz give the correct answer in your notebook and explain briefly and take brainliest mark

Answer 1

Hope u like my process
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For no current flow through the middle..

The whole system should follow the wheat stone bridge process
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Now whats wheat stone bridge..
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It's a system where the current flowing through the sides neutralizes and results in no current flow from middle and all this happens due to the resistances on their side..

Resistances in diagram is represented as p, q, r and s.

And by the hypothesis..
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It can be written as

$= > \boxed{ \green{ \bold{p \times r \: =q \times s} }}$
And,

$= > \boxed{ \green{ \bold{t = 0}}}$

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Now.. By problem..,

In position of q,
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The resistance at q should be given as (p×r/s) ohm

Now..

Calculating the resistance at q,
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$= > \it \: q = \blue{ \frac{p \times r }{s} } = \blue{ \frac{4 \times 4}{4} } = \bold{ \underline{ \blue{4 \: \: ohm}}}$
_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_

Now..

The equivalent resistance at q = 4 ohm and there are 2 resistance in parallel i.e. 8 and R respectively..

So...

Calculating R
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$= > \orange{ \bold{\frac{1}{q} }} = \bold{ \frac{1}{R}} \orange{ + \frac{1}{8} } \\ \\ = > \bold{ \frac{1}{R} = \orange{\frac{1}{4} - \frac{1}{8} } = \orange{\frac{1}{8} }} \\ \\ = > \boxed{ \bf {R} = \underline{ \it{ \orange{8 \: ohm}}}}$

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Thus, the required resistance(R) is 8 ohm
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Hope this is ur required answer

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