The above expression is obtained by using the fact that the voltage of the black box for a given current formula_2 is identical to the linear superposition of the solutions of the following problems: (1) to leave the black box open circuited but activate individual voltage source one at a time and, (2) to short circuit all the voltage sources but feed the circuit with a certain ideal voltage source so that the resulting current exactly reads formula_2 (Alternatively, one can use an ideal current source of current formula_2). Moreover, it is straightforward to show that formula_5 and formula_6 are the single voltage source and the single series resistor in question.