Question

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Answer 1

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Rules to be followed

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=> Equivalent resistance of resistors kept in series is the sum of all individual resistance.

$i.e. \: \: \: \: \: \bf \: r_{eq} = r_{1} + r_{2} + ...$

=> Equivalent resistance of resistors kept in parallel is the reciprocal of the sum of all reciprocal of all individual resistance.

$i.e. \: \: \: \bf \: \frac{1}{ r_{eq} } = \frac{1}{ r_{1} } + \frac{1}{ r_{2} } + ....$

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in step (1)

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We consider , all the series resistance at first , so

we can sum it up to

$= > \bf r_{eq} \degree = 4 + 8 = 12 \: ohm \\ \\ = > \bf r_{eq} \degree \degree = x + 5 = (x + 5) \: ohm$

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in step (2)

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we take the two parallel resistance and will find the equivalent resistance of total .

Here Req is given as 4 ohm

$= > \bf \frac{1}{ r_{eq} } = \frac{1}{ r_{eq} \degree} + \frac{1}{ r_{eq} \degree \degree} \\ \\ = > \frac{1}{ r_{eq} } = \frac{1}{12} + \frac{1}{x + 5} \\ \\ = > \frac{1}{4} = \frac{1}{12} + \frac{1}{x + 5} \\ \\ = > \frac{1}{x + 5} = \frac{1}{4} - \frac{1}{12} = \frac{3 - 1}{12} \\ \\ = > \frac{1}{x + 5} = \frac{2}{12} = \frac{1}{6} \\ \\ = > x + 5 = 6 \\ \\ = > \bf \: x = \it \: 5 - 6 = \bf \underline{ \blue{ \: 1 \: ohm}}$

So the required value of x is 1 ohm .

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