A combination consists of three resistors in series. Four similar sets are connected in parallel. If the resistance of each resistor is 2 ohm, find the resistance of the combination.

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Solution

Combination of three resistors, which are connected in series, $R_{s} = R_{1} + R_{2} + R_{3} = 2 + 2 + 2 = 6 Ω$

Now, four such branches are connected in parallel.

So, the net resistance $r$ is given by

$1 over r equals 1 over 6 plus fraction numerator begin display style 1 end style over denominator begin display style 6 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style 6 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style 6 end style end fraction equals 4 over 6 equals 2 over 3 r equals 3 over 2 equals 1.5 capital omega$

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