Two wires of same dimensions but resistivities ρ1 and ρ2 are connected in series. The equivalent resistivity of the combination is

Question

Two wires of same dimensions but resistivities ρ1 and ρ2 are connected in series. The equivalent resistivity of the combination is (A) 2(ρ1 + ρ2) (B) √ρ1ρ2 (C) (ρ1+ρ2/2) (D) 1/2(ρ1+ρ2)

Tardigrade Admin · Accepted Answer

R 1=(ρ1 l / A ) R 2=(ρ2 l / A ) R + R =(2 ρ l / A ) ∴ 2 R = R 1+ R 2 2 ρ=ρ1+ρ2 ∴ ρ=(1/2)(ρ1+ρ2)

Q. Two wires of same dimensions but resistivities $ρ_{1}$ and $ρ_{2}$ are connected in series. The equivalent resistivity of the combination is

$2 (ρ_{1} + ρ_{2})$

$ρ_{1} ρ_{2}$

$\frac{ρ _{1} + ρ _{2}}{2}$

$1/2 (ρ_{1} + ρ_{2})$

$R_{1} = \frac{ρ _{1} l}{A} R_{2} = \frac{ρ _{2} l}{A} R + R = \frac{2 ρl}{A} ∴ 2 R = R_{1} + R_{2} 2 ρ = ρ_{1} + ρ_{2} ∴ ρ = \frac{1}{2} (ρ_{1} + ρ_{2})$

Q. Two wires of same dimensions but resistivities ρ1​ and ρ2​ are connected in series. The equivalent resistivity of the combination is

2(ρ1​+ρ2​)

ρ1​ρ2​​

2ρ1​+ρ2​​

1/2(ρ1​+ρ2​)