Combination of Resistance
There are two ways of connecting the resistance that is, the series combination and is parallel combination.
Series Combination
The combination, in which the resistance are connected end to end with each other, is called series combination.
Let \[{{R}_{1}},\,\,{{R}_{2}}\] and \[{{R}_{3}}\] be three resistance, connected in series across a battery of potential V volt, as shown in the figure above. Now suppose \[{{V}_{1}}\] be the potential difference across the resistance \[{{R}_{1}};\,\,{{V}_{2}}\] be the potential difference across \[{{R}_{2}};\] and \[{{V}_{3}}\] be the potential difference across \[{{R}_{3}}\]. The total potential across the three resistance is given by
\[\mathbf{V=}{{\mathbf{V}}_{\mathbf{1}}}\mathbf{+}{{\mathbf{V}}_{\mathbf{2}}}\mathbf{+}{{\mathbf{V}}_{\mathbf{3}}}\]
But by Ohms law, \[V=I\times R\]
Since the same current I flows through the three resistance \[{{R}_{1}},\,\,{{R}_{2}}\]and \[{{R}_{3}}\], so by ohms law
\[{{V}_{1}}=I\times {{R}_{1}},\,\,{{V}_{2}}=I\times {{R}_{2}}\]and\[{{V}_{3}}=I\times {{R}_{3}}\]
Therefore, \[I\times R=I\times {{R}_{1}}+I\times {{R}_{2}}+I\times {{R}_{3}}\]
\[\Rightarrow \,\,I\times R=I\times
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