Series Connection:
When the cells are connected in series, the positive terminal of one cell is connected to the negative terminal of the next cell. This creates a closed loop through which the current flows.

Explanation:
1. Equivalent EMF: In a series connection, the total emf is the sum of the individual emfs of the cells. Therefore, the equivalent emf (E_eq) is given by E_eq = n * e, where n is the number of cells and e is the emf of each cell.

2. Equivalent Internal Resistance: In a series connection, the total internal resistance (r_eq) is also the sum of the individual internal resistances of the cells. Therefore, r_eq = n * r, where r is the internal resistance of each cell.

3. Total Current: According to Ohm's Law, the total current (I) flowing through the circuit is given by I = E_eq / (R + r_eq), where R is the external resistance connected to the circuit.

4. Conclusion: In a series connection, the total current is determined by the equivalent emf and the equivalent internal resistance of the cells. The number of cells does not affect the current flowing through the external resistance.

Parallel Connection:
When the cells are connected in parallel, the positive terminals of all cells are connected together, and the negative terminals are connected together. This creates multiple parallel paths for the current to flow through.

Explanation:
1. Equivalent EMF: In a parallel connection, the equivalent emf remains the same as the individual emf of each cell. Therefore, E_eq = e.

2. Equivalent Internal Resistance: In a parallel connection, the equivalent internal resistance (r_eq) can be calculated using the formula: 1/r_eq = 1/r + 1/r + ... + 1/r (n times), where r is the internal resistance of each cell and n is the number of cells.

3. Total Current: According to Ohm's Law, the total current (I) flowing through the circuit is given by I = E_eq / (R + r_eq), where R is the external resistance connected to the circuit.

4. Conclusion: In a parallel connection, the total current is determined by the equivalent emf and the equivalent internal resistance of the cells. The number of cells does not affect the current flowing through the external resistance.

Summary:
- In a series connection, the total current is determined by the equivalent emf and the equivalent internal resistance of the cells.
- In a parallel connection, the total current is also determined by the equivalent emf and the equivalent internal resistance of the cells.
- The number of cells does not affect the current flowing through the external resistance in either series or parallel connections.