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Series and Parallel Grouping of cell is considered one of the most asked concept.
40 Questions around this concept.
The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1, P2 and P3 respectively, then :
The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2\Omega$. The value of the internal resistance of each cell is
The current flowing through $3.25 \Omega$ resistance is
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5 cells of emf E and internal resistance r are connected in parallel giving 1A current. Then current from each cell is
If n cells are connected in series and such m connections are made in parallel then the potential difference across each cell is:
A house is served by a 220 V supply line in a circuit protected by a 9 ampere fuse. The maximum number of 60 W lamps in parallel that can be turned on, is
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
$\begin{aligned} & R=\frac{r}{n} \\ & P_{\max }=n\left(\frac{E^2}{4 r}\right)_{\text {when } r>>n R}\end{aligned}$
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