A cell can supply current of 0.4 A and 0.2 A through a 4.0Ω and 10.0Ω resistors respectively.

This internal resistance of the cell is

Answer Details

To find the internal resistance of the cell, we can use the formula:
Internal resistance (r) = (EMF - V) / I
where EMF is the electromotive force of the cell, V is the potential difference across the external resistor, and I is the current flowing through the circuit.
First, let's find the EMF of the cell. We know that the current through the 4.0Ω resistor is 0.4 A, so the potential difference across it is:
V = IR = 0.4 A x 4.0Ω = 1.6 V
Similarly, for the 10.0Ω resistor, we have:
V = IR = 0.2 A x 10.0Ω = 2.0 V
Now we can find the EMF by adding these potential differences:
EMF = V + IR = 1.6 V + 2.0 V = 3.6 V
Finally, we can use the formula above to find the internal resistance:
r = (EMF - V) / I = (3.6 V - 1.6 V) / 0.4 A = 2.0 Ω
Therefore, the internal resistance of the cell is 2.0Ω. Answer option A, "2.0Ω", is correct.