Calculating the EMF and Internal Resistance of a Cell
To find the minimum number of cells required to produce a current of 2 amperes in an external resistance of 4 ohms, we need to first calculate the EMF and internal resistance of a single cell.

Using Ohm's Law to Calculate Current
We can use Ohm's Law to calculate the current produced by a single cell:

I = E / (R + r)

Where I is the current, E is the EMF, R is the external resistance, and r is the internal resistance.

Solving for EMF and Internal Resistance
We know that we want the current to be 2 amperes and the external resistance to be 4 ohms. We also know that the internal resistance of each cell is 0.5 ohms.

So, we can set up the equation:

2 = E / (4 + 0.5)

Solving for E, we get:

E = 9 volts

Now that we know the EMF of each cell is 9 volts, we can calculate the number of cells needed to produce a current of 2 amperes.

Calculating the Number of Cells Needed
Each cell has an EMF of 9 volts and an internal resistance of 0.5 ohms. To produce a current of 2 amperes in an external resistance of 4 ohms, we need a total voltage of:

V = IR = 2 * 4 = 8 volts

To get a total voltage of 8 volts with cells that have an EMF of 9 volts each, we need:

N = V / E = 8 / 9 = 0.88

Since we can't have a fraction of a cell, we round up to get:

N = 1

Therefore, we need at least one cell with an EMF of 9 volts and an internal resistance of 0.5 ohms to produce a current of 2 amperes in an external resistance of 4 ohms.