Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination is

Question

Two metal wires of identical dimensions are connected in series. If σ1 and σ2 are the conductivities of the metal wires respectively, the effective conductivity of the combination is (A) (σ1+σ2/σ1σ2) (B) (σ1σ2/σ1+σ2) (C) (2σ1σ2/σ1+σ2) (D) (σ1+σ2/2σ1σ2)

Tardigrade Admin · Accepted Answer

here, R texteff = R 1+ R 2 or (( L + L )/σ texteff A )=( L /σ1 A )+( L /σ2 A ) (both wires are identical so have same cross section A ) Or (2/σ texteff )=(1/σ1)+(1/σ2) Or σ texteff =(2 σ1 σ2/σ1+σ2)

Q. Two metal wires of identical dimensions are connected in series. If $σ_{1}$ and $σ_{2}$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

$\frac{σ _{1} + σ _{2}}{σ _{1} σ _{2}}$

$\frac{σ _{1} σ _{2}}{σ _{1} + σ _{2}}$

$\frac{2 σ _{1} σ _{2}}{σ _{1} + σ _{2}}$

$\frac{σ _{1} + σ _{2}}{2 σ _{1} σ _{2}}$

here, $R_{eff} = R_{1} + R_{2}$
or $\frac{( L + L )}{σ _{eff} A} = \frac{L}{σ _{1} A} + \frac{L}{σ _{2} A}$
(both wires are identical so have same cross section $A$ )
Or $\frac{2}{σ _{eff}} = \frac{1}{σ _{1}} + \frac{1}{σ _{2}}$
Or $σ_{eff} = \frac{2 σ _{1} σ _{2}}{σ _{1} + σ _{2}}$

Q. Two metal wires of identical dimensions are connected in series. If σ1​ and σ2​ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

σ1​σ2​σ1​+σ2​​

σ1​+σ2​σ1​σ2​​

σ1​+σ2​2σ1​σ2​​

2σ1​σ2​σ1​+σ2​​