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 ` 4xx 10^(-3) Omega m` and it is 25 cm long while second material has resistivity of ` 5 xx 10^(-3) Omega m` and is of 70 cm long. Whati is the resistance of rod between its ends ?

Explanation

Resistivity ` rho = (RA)/l`
Resistance of first material
` R_1 = (rho_1 l_1)/(A_1)`
` R_1 = (4 xx10^(-3) xx25 xx10^(-2))/(9xx10^(-6))`
` = (100 xx 10^(-5 + 6))/9 = (1000)/9 = Omega`
Resistance of second material
` R_2 = (rho_2 l_2)/A_2 `
`R_2 =( 5xx 10^(-3) xx 70 xx 10^(-2))/( 9 xx10^(-6)) `
` = (350 xx 10^(-5 +6))/9`
` (3500)/9 Omega`
`:." "{:("Total"),("resistance R"_T):}} = 1000/9 + 3500/9`
`R_T = 4500/9 = 500 Omega`