# Two wires of equal diameters of resistivities  ρ1 and  ρ2 and length x1 and x2 respectively are joined in series …

Q: Two wires of equal diameters of resistivities  ρ1 and  ρ2 and length x1 and x2 respectively are joined in series . Find the equivalent resistivity of the combination.

Sol. Resistance, $\large R_1 = \rho_1 \frac{l_1}{A_1}$

$\large R_2 = \rho_2 \frac{l_2}{A_2}$

As the wires are of equal diameters A1 = A2 = A

R = R1 + R2

$\large \rho \frac{x}{A} = \rho_1 \frac{x_1}{A} + \rho_2 \frac{x_2}{A}$

$\large \rho x = \rho_1 x_1 + \rho_2 x_2$

$\large \rho ( x_1 + x_2 ) = \rho_1 x_1 + \rho_2 x_2$ (since , x = x1 + x2 )

$\large \rho = \frac{\rho_1 x_1 + \rho_2 x_2}{( x_1 + x_2 )}$