Two wires of equal diameters, of resistivities ${\rho _1}$ and ${\rho _2}$ and lengths $l_1$ and $l_2$, respectively, are joined in series. The equivalent resistivity of the combination is
Medium
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${R_1} = \frac{{{\rho _1}{l_1}}}{A}$ and ${R_2} = \frac{{{\rho _2}{l_2}}}{A}$.
In series ${R_{eq}} = {R_1} + {R_2}$
$\frac{{{\rho _{eq.}}({l_1} + {l_2})}}{A} = \frac{{{\rho _1}{l_1}}}{A} + \frac{{{\rho _2}{l_2}}}{A}$ $ \Rightarrow \,\,{\rho _{eq}} = \frac{{{\rho _1}{l_1} + {\rho _2}{l_2}}}{{{l_1} + {l_2}}}$.
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