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 cm . The value of ρ, to the nearest integer, is .

Question

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 cm . The value of ρ, to the nearest integer, is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/d5a1f99f35fc11a62af1160e2e377bb4-.png" /> R net =( R 1 R 2/ R 1+ R 2) (ρ ℓ/2 A )=(ρ1 (ℓ/ A ) × ρ2 (ℓ/ A )/ρ1 (ℓ) A +ρ2 (ℓ) A (ρ/2)=(6 × 3/6+3)=2 ρ=4

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

$R_{n e t} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$
$\frac{ρ ℓ}{2 A} = \frac{ρ _{1} \frac{ℓ}{A} \times ρ _{2} \frac{ℓ}{A}}{ρ _{1} \frac{ℓ}{A} + ρ _{2} \frac{ℓ}{A}}$
$\frac{ρ}{2} = \frac{6 \times 3}{6 + 3} = 2$
$ρ = 4$

Q. Two wires of same length and thickness having specific resistances 6Ωcm and 3Ωcm respectively are connected in parallel. The effective resistivity is ρΩcm. The value of ρ, to the nearest integer, is _______.

Rnet​=R1​+R2​R1​R2​​ 2Aρℓ​=ρ1​Aℓ​+ρ2​Aℓ​ρ1​Aℓ​×ρ2​Aℓ​​ 2ρ​=6+36×3​=2 ρ=4

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

$R_{n e t} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$
$\frac{ρ ℓ}{2 A} = \frac{ρ _{1} \frac{ℓ}{A} \times ρ _{2} \frac{ℓ}{A}}{ρ _{1} \frac{ℓ}{A} + ρ _{2} \frac{ℓ}{A}}$
$\frac{ρ}{2} = \frac{6 \times 3}{6 + 3} = 2$
$ρ = 4$