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the sentence

The system can only operate in equilibrium where the line and the curve intersect – the voltage and current in the resistor have to be the same as the leakage voltage and current. 

should say

The system can only operate in equilibrium where the line and the curve intersect – the current in the resistor has to be the same as the leakage current. 

That is only the current in the resistor and the output stage have to be same as they are in series.

The voltage adjusts itself across both to make the currents the same.