If the internal resistance of a cell is 20 ohm and the resistance of the circuit is also 20 ohm. Will the current remain the same where the given n identical cells are in series or in parallel?

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Solution

Step1: Given data
There are n identical cells and each has an internal resistance of $20 o h m$ . The resistance of the circuit is also $20 o h m$ .
Step2: Resistance
The property of materials that allows the flow of electric current is known as resistance.
The movement of the stream is surely opposed by resistance.
Furthermore, ohms $Ω$ is the unit of resistance.
The resistance of a resistor is determined by the voltage across it and the current flowing through it.
Resistance is a measurement of the resistance to current flow in an electrical circuit.
Step3: Internal resistance
When electricity travels via a circuit, the cell's internal resistance resists current flow.
Step4: Formula used
If n cells of e.m.f. $V_{1}, V_{2}, V_{3}, . . .$ are connected in series, then the effective e.m.f. is $V_{1} + V_{2} + V_{3} + . . . + V_{n}$
If n cells of e.m.f. $V_{1}, V_{2}, V_{3}, . . .$ are connected in parallel then the effective e.m.f. is $\frac{V_{1} + V_{2} + V_{3} + . . . + V_{n}}{n}$
Step5: Calculating current in series and in parallel
Let e.m.f. of each cell is V.
Case I- Consider the given n cells are connected in series. Then effective $e . m . f . = n V$
Since cells are connected in series, the internal resistances are also in series connection. The net internal resistance is $r_{e f f} = 20 n$ .
The resistance in the circuit is $R = 20 Ω$
The current flowing through the circuit is $I_{s} = \frac{e f f e c t i v e e m f}{r_{e f f} + R} = \frac{n V}{20 n + 20}$
Case I- Consider the given n cells are connected in series. Then effective $e . m . f . = V$
Since cells are connected in parallel, the internal resistances are also in parallel connection. The net internal resistance is $r_{e f f} = \frac{20}{n}$
The current flowing through the circuit is $I_{P} = \frac{e f f e c t i v e e m f}{r_{e f f} + R} = \frac{V}{\frac{r}{n} + R} = \frac{n V}{r + n R} = \frac{n V}{20 + 20 n}$
Now compare the current obtained in both the cases. $I_{s} = I_{P}$
Hence, the current remains the same where the given n identical cells are in series or in parallel.

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