Two wires of same radius having lengths `l_1`, and `l_2` and resistivities `rho_1` and `rho_2` are connected in series. The equivalent resistivity will be

Options

A. `(rho_1 l_2 + rho_2 l_1)/( rho _1 + rho_2)`
B. `(rho_1 l_1 + rho_2 l_2)/( l _1 +l _2)`
C. `(rho_1 l_1 + rho_2 l_2)/( l _1 - l_2)`
D. `(rho_1 l_2 + rho_2 l_1)/( l _1 + l_2)`

Answer

B

Explanation

In series equivalent resistances
` R = R_1 +R_2`
hence ` R_1 =( rho _1 l_1)/(A) .R_2 = ( rho _2 l_2) /(A) , R = (rho (l_1 +l_2))/( A)`
` therefore (rho (l_1 +l_2))/(A) =( rho _1 l_1 )/( A) + (rho _1 l_1)/(A) +( rho _1 l_2)/( A) = rho = (rho _1 l_1 +rho_2 l_2)/( l_1 l_2)`