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

Group of cell is called a battery.

In series grouping of cell's their emf's are additive or subtractive while their internal resistances are always additive. If dissimilar plates of cells are connected together their emf's are added to each other while if their similar plates are connected together their emf's are subtractive.

(1) Series grouping : In series grouping anode of one cell is connected to cathode of other cell and so on. If n identical cells are connected in series

(i) Equivalent emf of the combination \[{{E}_{eq}}=nE\]

(ii) Equivalent internal resistance \[{{r}_{eq}}=nr\]

(iii) Main current = Current from each cell \[=i=\frac{nE}{R+nr}\]

(iv) Potential difference across external resistance \[V=iR\]

(v) Potential difference across each cell \[V'=\frac{V}{n}\]

(vi) Power dissipated in the external circuit \[={{\left( \frac{nE}{R+nr} \right)}^{2}}.\,R\]

(vii) Condition for maximum power \[R=nr\] and \[{{P}_{\max }}=n\,\left( \frac{{{E}^{2}}}{4r} \right)\]

(viii) This type of combination is used when \[nr<<R\].

(2) Parallel grouping : In parallel grouping all anodes are connected at one point and all cathode are connected together at other point. If n identical cells are connected in parallel

(i) Equivalent emf \[{{E}_{eq}}=E\]

(ii) Equivalent internal resistance \[{{R}_{eq}}=r/n\]

(iii) Main current \[i=\frac{E}{R+r/n}\]

(iv) potential difference across external resistance = p.d. across each cell \[=V=iR\]

(v) Current from each cell \[i'=\frac{i}{n}\] 

(vi) Power dissipated in the circuit \[P={{\left( \frac{E}{R+r/n} \right)}^{2}}.\,R\]

(vii) Condition for max. power is \[R=r/n\] and \[{{P}_{\max }}=n\,\left( \frac{{{E}^{2}}}{4r} \right)\]

(viii) This type of combination is used when \[nr>>R\]

(3) Mixed Grouping : If n identical cell's are connected in a row and such m row's are connected in parallel as shown.

(i) Equivalent emf of the combination\[{{E}_{eq}}=nE\]

(ii) Equivalent internal resistance of the combination \[{{r}_{eq}}=\frac{nr}{m}\]

(iii) Main current flowing through the load \[i=\frac{nE}{R+\frac{nr}{m}}=\frac{mnE}{mR+nr}\]

(iv) Potential difference across load \[V=iR\]

(v) Potential difference across each cell \[V'=\frac{V}{n}\]

(vi) Current from each cell \[i\,'=\frac{i}{n}\]

(vii) Condition for maximum power \[R=\frac{nr}{m}\] and\[{{P}_{\max }}=(mn)\frac{{{E}^{2}}}{4r}\]

(viii) Total number of cell \[=mn\]