# Why in the Thevenin Theorem do we have to “turn off” independent sources to find Thevenin resistance

In my basic circuits course we learned a handy circuit analysis technique so that we can simplify a linear circuit to it's equivalent voltage source and resistance.

When looking for the Thevenin resistance I wad told to turn off all independent sources.

Why do we do this (proof wise).

Also why don't we turn off dependent sources too?

Say you connect a voltage source Va at the external terminals across which you want to find the the equivalent resistance. Now if you change the voltage Va, voltage across the elements in the network changes, so does the current. The ratio of this change in voltage to that of current, $$\\Delta V/\Delta I\$$ is the equivalent resistance offered by that element.

The total resistance of a network can be calculated by replacing each element by its equivalent resistance.

• For a reistor, $$\\Delta V/\Delta I\$$ will be its resistance value only.

• Since voltage across an independent voltage won't change ($$\\Delta V=0\$$), its equivalent resistance will be zero. Hence it can be replaced by a short. Similarly, independent current source ($$\\Delta I=0\$$) can be replaced by an open circuit. Which is basically 'switching off' these sources.

• But for dependent sources, this $$\\Delta V/\Delta I\$$ ratio need not be zero or infinity as the value of source depends on voltage/current at some other node/branch in the network. Hence effectively it can have a non zero finite resistance to offer and hence can not be 'switched off'.

• ? I don't understand how dependent sources can have non zero finite resistance.. – Nick Yarn Oct 29 '18 at 16:21
• @NickYarn, you could say a resistor is a VCCS that just happens to have its control terminals and output terminals connected to the same 2 nodes. Other connection patterns are fussier to find the effect of, but they still have the possibility of changing a network port's current in response to a change in the port voltage. – The Photon Oct 29 '18 at 16:35
• @NickYarn I have modified the answer. Let me know if you still have problem. – nidhin Oct 29 '18 at 16:57
• Thanks for the explanation, however I'd like to know how this statement is true. "The total resistance of a network can be calculated by replacing each element by its equivalent resistance. " – Nick Yarn Oct 30 '18 at 5:26
• @NickYarn the idea behind that statement is that if you have a network with only resistors, you can find the total resistance by ‘combining them’ (parallel, series combinations). But if you have other elements, then replace them with their equivalent resistance to do so. Sorry if the statement was misleading. – nidhin Oct 30 '18 at 5:37