A ring is made of wire having a resistance R_o = 12Ω. 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 subcircuit between these points is equal to 8/3Ω

$straight l subscript 1 over straight l subscript 2 space equals 5 over 8$
$straight l subscript 1 over straight l subscript 2 space equals space 1 third$
$straight l subscript 1 over straight l subscript 2 space equals space 3 over 8$
$straight l subscript 1 over straight l subscript 2 space equals 1 half$

Solution

straight l subscript 1 over straight l subscript 2 space equals 1 half

We space knows space straight R proportional to straight I Here comma space straight R subscript 1 plus straight R subscript 2 space equals 12 straight capital omega and space fraction numerator straight R subscript 1 plus straight R subscript 2 over denominator straight R subscript 1 plus straight R subscript 2 end fraction space equals space 8 over 3 straight capital omega rightwards double arrow space straight R subscript 1 straight R subscript 2 space equals space 32 space straight capital omega We space get comma space straight R subscript 1 space equals space 8 space and space straight R subscript 2 space equals space 4 Again comma space straight R subscript 1 space equals space fraction numerator 12 space straight l subscript 1 over denominator straight l subscript 1 plus straight l subscript 2 end fraction and space straight R subscript 2 space equals fraction numerator 12 space straight l subscript 2 over denominator straight l subscript 1 plus straight l subscript 2 end fraction Hence comma space fraction numerator straight l subscript 1 over denominator straight l subscript 2 space end fraction space equals 1 half

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