Question

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

• A. $\sigma _ { 1 } + \sigma _ { 2 }$
• B. $\frac { \sigma _ { 1 } + \sigma _ { 2 } } { 2 }$
• C. $\sqrt { \sigma _ { 1 } \sigma _ { 2 } }$
• D. $\frac { 2 \sigma _ { 1 } \sigma _ { 2 } } { \sigma _ { 1 } + \sigma _ { 2 } }$

Answer 1

Answer: (D)

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

Answer 2

: Resistance of a wire in terms of conductivity is given by

where l is the length and A is the area of cross – section of wire respectively.

As the wires are onnected in series,

$\therefore \mathrm { R } _ { \mathrm { s } } = \mathrm { R } _ { 1 } + \mathrm { R } _ { 2 }$

where is the effective conductivity