The DC emf is 24 V. When connected to an external resistance of 10 Ohm

The DC emf is 24 V. When connected to an external resistance of 10 Ohm, the current in the circuit was 2 A. Determine the resistance of the current source.

Let’s introduce the notation:

I is the current strength, measured in Amperes (A).
U is the voltage, measured in Volts (V).
R is the external resistance of the circuit, measured in ohms (ohms).
r – internal resistance or resistance of the current source, also measured in Ohms (Ohm).
E – EMF of the current source, like voltage, is measured in Volts (V).
Ohm’s law for a section of a circuit states that the current is directly proportional to the voltage and inversely proportional to the electrical resistance: I = U / R.
However, if the resistance of the current source (r) also appears in the problem, then another form of Ohm’s law should be applied here – for a complete circuit: I = E / (R + r). As can be seen from the written formula, the voltage is no longer here, the letter “E” means EMF – electromotive forces, and the resistance of the current source is also added to the external resistance. Knowing Ohm’s law for a complete circuit, we will solve our problem using known quantities.

Find the resistance of the current source from Ohm’s law for a complete circuit
Let us express from the formula I = E / (R + r) the resistance of the current source:
r = (E / I) – R, and then just substitute the initial data into the resulting formula: E = 24 V, R = 10 Ohm, I = 2 A. Thus, we get: r = (24/2) – 10 = 12 – 10 = 2 ohms.
Answer: r = 2 ohms.