Category : JEE Main & Advanced
(1) Series grouping
(i) Same current flows through each resistance but potential difference distributes in the ratio of resistance i.e. \[V\propto R\]
(ii) \[{{R}_{eq}}={{R}_{1}}+{{R}_{2}}+{{R}_{3}}\] equivalent resistance is greater than the maximum value of resistance in the combination.
(iii) If n identical resistance are connected in series \[{{R}_{eq}}=nR\] and potential difference across each resistance \[V'=\frac{V}{n}\]
(2) Parallel grouping
(i) Same potential difference appeared across each resistance but current distributes in the reverse ratio of their resistance i.e. \[i\propto \frac{1}{R}\]
(ii) Equivalent resistance is given by \[\frac{1}{{{R}_{eq}}}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}\] or \[{{R}_{eq}}={{(R_{1}^{-1}+R_{2}^{-1}+R_{3}^{-1})}^{-1}}\] or \[{{R}_{eq}}=\frac{{{R}_{1}}{{R}_{2}}{{R}_{3}}}{{{R}_{1}}{{R}_{2}}+{{R}_{2}}{{R}_{3}}+{{R}_{2}}{{R}_{1}}}\]
Equivalent resistance is smaller than the minimum value of resistance in the combination.
(iv) If two resistance in parallel
\[{{R}_{eq}}=\frac{{{R}_{1}}{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}=\frac{\text{Multiplication}}{\text{Addition}}\]
(v) Current through any resistance
\[i\,'=i\times \left[ \frac{\text{Resistance of opposite branch}}{\text{Total resistance }} \right]\]
Where \[i'=\] required current (branch current), \[i=\]main current
\[{{i}_{1}}=i\,\left( \frac{{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}} \right)\]
and \[{{i}_{2}}=i\,\left( \frac{{{R}_{1}}}{{{R}_{1}}+{{R}_{2}}} \right)\]
(vi) In n identical resistance are connected in parallel \[{{R}_{eq}}=\frac{R}{n}\] and current through each resistance \[i'=\frac{i}{n}\]
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