Equivalent Resistance with Dependent Source

This circuit exhibits a negative resistance from the terminal at the 10 kOhm resistor to ground. When the -5 V source is active and the test voltage (1 V source) is disconnected, it has V_Th = 10 V. To measure R_th, we can deactivate the independent source (flip the switch to ground) and apply a test voltage (connect the switch on the right). The resistance is the applied voltage divided by how much current goes _into_ the terminal. Note that 200 uA comes _out_ of the terminal - a result of the depwendent source reacting to the applied voltage. Therefore the equivalent resistance "looking into" that terminal is R_Th = V_x/I_x = 1 V / -200 uA = -5 kOhm. This unintuitive result can be achieved in practice using opamps.

published 1 year ago