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

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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 $ρ$ to the nearest integer, is______

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answer is 4.

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Detailed Solution

Specific Resistance is called resistivity.

If length of each resistance is ‘ $l$ ’ then $R_{1} = \frac{6 l}{A}$ and $R_{2} = \frac{3 l}{A}$ .

Equivalent resistance in parallel combination is,

$R = \frac{R_{1} R_{2}}{R_{1} + R_{2}} \Rightarrow \frac{ρ l}{2 A} = \frac{(\frac{6 l}{A}) (\frac{3 l}{A})}{(\frac{6 l}{A}) + (\frac{3 l}{A})} \Rightarrow \frac{ρ}{2} = 2 \Rightarrow ρ = 4 Ω c m$