Question

five cells each of emf E and resistance r are connected in series. due to oversight one cell is connected wrongly. the equivalent emf and internal resistance of the combination is

Answer 1

Emf of the 5 identical cells of emf E are connected in series. Then the net emf of the combination should be 5E.

But, one of them is wrongly connected i.e. with its polarity reversed. This cell will cancel the emf of another cell.

Thus, equivalent number of cells in the combination = E + E + E + E - E = 3E. Net emf of the combination = 3E.

However, internal resistance of all the cells connected in series will add up irrespective of the fact that two of the cells are wrongly connected. Net internal resistance of the combination = 5r.

Ans 3E, 5r.

Answer 2

The equivalent EMF will be 3E and the equivalent resistance will be 5r.

Five cells of EMF E and resistance r are connected in series, but one cell is connected in the opposite direction.

Therefore as they are in series, the EMF will get added to get the equivalent EMF of the circuit. Hence the equivalent EMF of the circuit is

$EMF= E+E+E+E-E=3E$

The one negative sign is because one cell is connected in the opposite direction.

The internal resistances are also in series. Therefore the net equivalent resistance will be $r+r+r+r+r=5r$.

The net EMF is 3E and the equivalent resistance is 3r.

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