The EMF of the direct current source is 12 V, and its internal resistance is 0.5 Ohm.

The EMF of the direct current source is 12 V, and its internal resistance is 0.5 Ohm. At what external resistance of the circuit will the current be equal to 2 A?

Ohm’s law for a complete circuit:

I = e / (R + r), where I is the current in the circuit
e- EMF of the voltage source
r- internal resistance of the voltage source
R- total external resistance of the circuit

Let’s transform the formula:
I = e / (R + r)
R + r = e / I
R = e / I – r

R = 12 [B] / 2 [A] – 0.5 [Ohm]
R = 5.5 [Ohm]