Name: Applications of Potentiometer
Uploaded: 2019-07-19
Duration: 4 min 30 s
Description: Since potentiometers are very versatile and handy to use, it is vital to understand their working principle and applications fully. In this video, learn abou...

Question

Explain with circuit diagram the parallel combination of identical cells. Obtain the condition for maximum current in the external resistance connected with the combination.

Accepted Answer

Considering $m$ identical cells: $C_{1}$ , $C_{2}$ , ..., $C_{m}$

All the cells are having emf of $E$ and internal resistance $r$ and connected to an external resistance $R$ parallelly.

As per the arrangement of cells, the equivalent emf of all the cells is equal to emf of a single cell, that is, $E_{e f f} = E$

The equivalent resistance of all the cells: $\frac{1}{r_{e f f}} = \frac{1}{r} + \frac{1}{r} + . . . + \frac{1}{r} = m \frac{1}{r} \Rightarrow r_{e f f} = \frac{r}{m}$

So the total resistance in the circuit: $R_{n e t} = r_{e f f} + R = \frac{r}{m} + R$

The current flowing through the circuit: $I = \frac{E}{R_{n e t}} = \frac{E}{\frac{r}{m} + R} = \frac{m E}{r + m R}$

If $R < < r$ then we can neglect $R$ in the above circuit then maximum current can be observed that will be $I = \frac{m E}{r}$ .

Explain with circuit diagram the parallel combination of identical cells. Obtain the condition for maximum current in the external resistance connected with the combination.

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