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NEET 2012 (AIPMT, Prelims) · Combination of Resistors

Combination of Resistors question from NEET 2012 (AIPMT, Prelims)

Q72NEET 2012 · AIPMT · PRELIMSMedium

Combination of Resistors

A ring is made of a wire having a resistance R0 = 12 $\Omega$ . Find the points A and B, as shown in the figure, at which a current carrying conductor should be connected so that the resistance R of the sub circuit between these point is equal to $\frac{8}{3}\Omega$ .

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Answer: (d)

Let the arcs be $R_1$ and $R_2$ : $R_1 + R_2 = 12$ and $\dfrac{R_1 R_2}{12} = \dfrac{8}{3}$ , so $R_1R_2 = 32$ .
Solving: $R_1 = 4\ \Omega$ , $R_2 = 8\ \Omega$ .
$R \propto l$ , so $\dfrac{l_1}{l_2} = \dfrac{4}{8} = \dfrac{1}{2}$
So the answer is (d).

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