Consider N = n₁ n₂ identical cells, each having an emf E and an internal resistance r . Assume n₁ cells are connected in series to form a line, and n₂ such lines are connected in parallel. This combination supplies current to an external resistance R . Determine the current flowing through the external resistance.

Step-by-step solution

For a single line of n₁ cells connected in series, the equivalent emf is n₁ E and the equivalent internal resistance is n₁ r . When n₂ such lines are connected in parallel, the equivalent emf of the entire combination remains equal to the emf of a single line, which is E _ eq = n₁ E . The equivalent internal resistance of n₂ parallel lines, each of resistance n₁ r , is r_ eq = n₁ r n₂ . The total current I flowing through the external resistance R is given by I = E _ eq R + r_ eq . Substituting the values, we get I