The EMF of the current source is 30 V, and its internal resistance is 2 ohms.

The EMF of the current source is 30 V, and its internal resistance is 2 ohms. Determine the load resistance if the full power that it emits, the source is 90 W.

EMF = 30 V.
r = 2 ohms.
N = 90 W.
R -?
The current power is determined by the formula: N = I * EMF, where I is the current strength, EMF is the electromotive force of the current source.
Let’s write Ohm’s law for a complete closed circuit: I = EMF / (r + R), where r is the internal resistance of the current source, R is the external resistance.
N = I * EMF = EMF ^ 2 / (r + R).
r + R = EMF ^ 2 / N.
R = EMF ^ 2 / N – r.
R = (30V) ^ 2 / 90W – 2 ohms = 8 ohms.
Answer: the resistance of the external load is R = 8 ohms.