Two wires of equal diameters,lengths l_1, l_2 | vedclass

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(A) The resistance of a wire is given by $R = \frac{S l}{A}$,where $S$ is resistivity,$l$ is length,and $A$ is the cross-sectional area.Since the wire

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$\frac{S_1 l_1+S_2 l_2}{l_1+l_2}$

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(A) The resistance of a wire is given by $R = \frac{S l}{A}$,where $S$ is resistivity,$l$ is length,and $A$ is the cross-sectional area.Since the wires are joined in series,the total resistance $R$ is the sum of individual resistances: $R = R_1 + R_2$.Substituting the formula for resistance: $\frac{S(l_1 + l_2)}{A} = \frac{S_1 l_1}{A} + \frac{S_2 l_2}{A}$.Since the diameters are equal,the cross-sectional area $A$ is the same for both wires.Canceling $A$ from both sides,we get: $S(l_1 + l_2) = S_1 l_1 + S_2 l_2$.Therefore,the equivalent resistivity $S$ is: $S = \frac{S_1 l_1 + S_2 l_2}{l_1 + l_2}$.

Two wires of equal diameters,lengths $l_1, l_2$ and having resistivities $S_1, S_2$ respectively are joined in series. The equivalent resistivity of the combination is

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