JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर Grouping of Resistance

(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 \[i'=\frac{i}{n}\]