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Because these are conceptual schematics, where possible I have used convenient decimal values of the quantities - 1 or 10 [V, mA, kohm]. This simplifies the calculations since [mA].[kohm] = [V].

As usual, I have accompanied my step-by-step explanations with CircuitLab simulations. In order not to clutter schematics with measuring devices, I completely rely on the attractive DC live simulation. For this purpose, hover the mouse over the circuit and see the local voltages and currents.

We can check it very easily by replacing the voltage source with a piece of wire. As we can see, the current continues flowing. So, we conclude, the CircuitLab current source is a true current source that contains energy inside.

As usual, I have accompanied my step-by-step explanations with CircuitLab simulations. In order not to clutter schematics with measuring devices, I completely rely on the attractive DC live simulation. For this purpose, just hover the mouse over the circuit and see the local voltages and currents.

We can check it very easily by replacing the voltage source with a piece of wire. As we can see, the current continues flowing and the voltage across it reverses its polarity. So, we conclude, the CircuitLab current source is a true current source that contains energy inside.

We can swap the role of the voltage source and the resistor making V varying and R constant.

We can swap the role of the voltage source and the resistor making V varying and R constant. For example, the op-amp inverting current source acts this way.