jaipreet singh asked: “can you please tell me the DERIVATION OF CELLS IN SERIES AND PARALLEL?”
Answer: I am posting here the simplified treatment to calculate the current in a circuit with combination of cells.
In this derivation it is assumed that all cells have the same EMF and same internal resistance.
CELLS IN SERIES
Consider n identical cells of emf E and internal resistance r connected in series across an external resistor of resistance R.
The total internal resistance = nr (since the internal resistances come in series)
The total resistance in the circuit = nr+R
The total emf = nE (since the emfs add up in series circuit)
Therefore, the current in the circuit;
PARALLEL COMBINATION OF CELLS
Consider m identical cells of emf E and internal resistance connected in parallel across an external resistor of resistance R.
The total emf in circuit = E (Since each cell has the same emf and they are in parallel)
The net internal resistance = r/m (since the cells are in parallel, their resistances are also in parallel. If m identical resistances are in parallel, the effective resistance is r/m)
The total resistance in circuit = R + r/m
Therefore, the current in circuit;
MIXED COMBINATION OF CELLS
Consider a combination of m rows of n cells each. The emf of each cell is E and the internal resistance of each cell is r. This combination is connected across and external resistance R.
The total EMF = nE
The net internal resistance = nr/m
The total resistance in circuit = R + nr/m
The current in circuit;