The battery consists of elements connected in series with each other with a resistance of 0.2

The battery consists of elements connected in series with each other with a resistance of 0.2 Ohm and an EMF of 0.5 V each. With a current in the external circuit of 2 A, the useful power of the battery is 1 W. How many cells are in the battery?

Let the number of elements be n. Then the EMF of the battery will be equal to nE, where E is the EMF of one cell. The internal resistance of the battery is nr, where r is the internal resistance of one cell.
Ohm’s law for the circuit under consideration will be written in the form:
I = nE / (R + nr) (1),
where R is external resistance, I is current.
R is found by the known values of current and power:
P = I ^ 2 * R;
R = P / I ^ 2;
R = 1 W / 4 A ^ 2 = 0.25 Ohm.
Substitute the values from the condition into (1):
2 A = (n * 0.5 V) / (0.25 Ohm + n * 0.2 Ohm);
2 A * 0.25 Ohm + 2 A * 0.2 Ohm * n = 0.5 V * n;
0.5V + 0.4V * n = 0.5V * n;
0.5 V = 0.1 V * n;
n = 5.

Answer: 5 elements.