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Physics-

General

Easy

Question

In the circuit shown here, what is the value of the unknown resistor R so that the total resistance of the circuit between points P and Q is also equal to R

3 ohms
$\sqrt{39} o h m s$
$\sqrt{69} o h m s$
10 ohms

The correct answer is: $square root of 69 o h m s$

The given circuit can be simplified as follows

$R equals 3 plus fraction numerator 10 cross times left parenthesis 3 plus R right parenthesis over denominator 10 plus 3 plus R end fraction equals 3 plus fraction numerator 30 plus 10 R over denominator 13 plus R end fraction$
$R equals fraction numerator 39 plus 3 R plus 30 plus 10 R over denominator 13 plus R end fraction equals fraction numerator 69 plus 13 R over denominator 13 plus R end fraction$
$13 R plus R to the power of 2 end exponent equals 69 plus 13 R$ Þ $R equals square root of 69 capital omega$ .

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