Two wires of the same dimensions but resistivities ${\rho _1}$ and ${\rho _2}$ are connected in series. The equivalent resistivity of the combination is
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Two cells, having the same $e.m.f.$ are connected in series through an external resistance $R.$ Cells have internal resistances $r_1$ and $r_2\,\, (r_1 > r_2)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of $R$ is
$n$ identical cells are joined in series with its two cells $A$ and $B$ in the loop with reversed polarities. $EMF$ of each shell is $E$ and internal resistance $r$. Potential difference across cell $A$ or $B$ is (here $n > 4$)
Two conductors have the same resistances at $0^{\circ} \mathrm{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :