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 $E_{e q}=n E$
- Equivalent internal resistance $r_{e q}=n r$
- Main current / current from each cell $i=\frac{n E}{R+n r}$
- Power dissipated in the external circuit is $\left(\frac{n E}{R+n r}\right)^2 \cdot R$
- Conditions for Maximum Power is $R=n r$
- $P_{\text {max }}=n\left(\frac{E^2}{4 r}\right)$ when $n r<R$

 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 $E_{e q}=E$
Equivalent internal resistance $R_{e q}=\frac{r}{n}$
The main current is

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

$
V=i R
$
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

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