Grouping Of Cells - Practice Questions & MCQ

 series grouping of cell:

In series grouping anode of one cell is connected to the cathode of other cells

$n=$ identical cells which are connected in series, then
- Equivalent e.m.f of combination is $E_{eq}=nE$
- Equivalent internal resistance $r_{eq}=nr$
- Main current / current from each cell $i=\frac{nE}{R+nr}$
- Power dissipated in the external circuit is ${\left(\frac{nE}{R+nr}\right)}^2\cdot R$
- Conditions for Maximum Power is $R=nr$
- $P_{\text{max }}=n\left(\frac{E^2}{4r}\right)$ when $nr<R$

 Parallel grouping of cell

In parallel grouping, all anodes are connected to one point and all cathode together at other points

For n cells connected in parallel
Equivalent e.m.f $E_{eq}=E$
Equivalent internal resistance $R_{eq}=\frac{r}{n}$
The main current is

$i=\frac{E}{R+\frac{r}{n}}$
The potential difference across the external resistance

$V=iR$
Current from each cell

$i^{\prime }=\frac{i}{n}$

The power dissipated in the circuit

$P={\left(\frac{E}{R+\frac{r}{n}}\right)}^2\cdot R$

Condition for Maximum Power

$\begin{array}{rl}& R=\frac{r}{n}\\ & P_{max}=n{\left(\frac{E^2}{4r}\right)}_{\text{when }r>>nR}\end{array}$