Question

explain parallel combination of cell

Answer 1

The explanation describes the parallel combination of cells, deriving the effective EMF ($E_{eff} = E$), effective internal resistance ($r_{eff} = r/n$), and the current through an external resistance ($I = \frac{nE}{nR + r}$). It is useful when internal resistance is high or higher current capacity is needed.

Answer 2

Explanation of Parallel Combination of Cells

When cells are connected in parallel, all the positive terminals are connected together, and all the negative terminals are connected together. This arrangement provides a path for current to flow through each cell simultaneously.

Consider 'n' identical cells, each with an electromotive force (EMF) 'E' and internal resistance 'r', connected in parallel to an external resistance 'R'.

1. Effective EMF: In a parallel combination of identical cells, the potential difference across the combination is equal to the EMF of a single cell.
   Effective EMF, $E_{eff} = E$.

2. Effective Internal Resistance: The internal resistances of the cells are connected in parallel. For 'n' identical resistances 'r' in parallel, the equivalent internal resistance $r_{eff}$ is given by:
   $\frac{1}{r_{eff}} = \frac{1}{r} + \frac{1}{r} + ... \text{(n times)}$
   $\frac{1}{r_{eff}} = \frac{n}{r}$
   $r_{eff} = \frac{r}{n}$

3. Current in the External Circuit: The total resistance in the circuit is the sum of the external resistance 'R' and the effective internal resistance $r_{eff}$.
   Total resistance, $R_{total} = R + r_{eff} = R + \frac{r}{n}$.
   Using Ohm's Law, the current 'I' flowing through the external circuit is:
   $I = \frac{\text{Effective EMF}}{\text{Total Resistance}} = \frac{E}{R + \frac{r}{n}}$
   $I = \frac{nE}{nR + r}$

4. Usefulness: The parallel combination is particularly useful when:

   • The internal resistance of the cells ('r') is high compared to the external resistance ('R'). In this case, $R + \frac{r}{n}$ is significantly smaller than $R+r$ (current from a single cell), leading to a larger total current output. $I = \frac{nE}{nR + r}$. If $r >> R$, then $I \approx \frac{nE}{r}$.
   • A larger current capacity is required. The total current drawn from the combination is shared among the individual cells ($I = i_1 + i_2 + ... + i_n$), reducing the current through each cell and potentially increasing the overall lifespan or capacity delivered at a high discharge rate.