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Q.

Two wires of same length and thickness having specific resistances $6 Ω$ cm and $3 Ω$ cm respectively are connected in parallel. The effective resistivity is $ρ Ω c m$ . The value of $ρ$ , to the nearest integer, is______

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answer is 4.

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Detailed Solution

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If length of each resistance is ‘ $l$ ’ then $R_{1} = 6 l$ and $R_{2} = 3 l$ . Equivalent resistance in parallel combination is, $R = \frac{R_{1} R_{2}}{R_{1} + R_{2}} \Rightarrow R = \frac{(6 l) (3 l)}{(6 l) + (3 l)} = 2 l$
So, effective resistivity is $2 Ω$ cm

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