The rod given in the figure is made up of two different materials.

Both have square cross sections of 3 mm side. The resistivity of the first material is `4xx10^(-3)Omega.m` and it is 25 cm long while second material has resistivity of `5xx10^(-3)Omega.m` and is of 70 cm long. What is the resistivity of rod between its ends?

Explanation

Square cross section of side, `a=3 m m=3xx10^(-3)m`
Cross section of side, `A=a^(2)=9xx10^(-6)m`
First material:
Resistivity of the material, `rho_(1)=4xx10^(-3)Omega m`
length, `l_(1)=25cm=25xx10^(-2)m`
Resistance of the rod, `R_(1)=(rho_(1)l_(1))/(A)=(4xx10^(-3)xx25xx10^(-2))/(9xx10^(-6))=(100xx10^(-5)xx10^(6))/(9)`
`R_(1)=11.11xx10^(1)Omega`
Second material:
Resistivity of the material, `rho_(2)=5xx10^(-3)Omega m`
length, `l_(2)=70cm=70xx10^(-2)m`
Resistance of the rod, `R_(2)=(rho_(2)l_(2))/(A)=(5xx10^(-3)xx70xx10^(-2))/(9xx10^(-6))=(350xx10^(-5)xx10^(6))/(9)`
`R_(2)=38.88xx10^(1)`
`R_(2)=389Omega`
Total resistance between the ends f the rods
`R=R_(1)+R_(2)=111+389`
`=500Omega`