# Thevenin's Equivalent Resistance

#### clubgitmo

Joined Oct 31, 2013
1
Howdy Guys -

I'm in a basic circuit analysis class. I'm having difficulty consistently calculating Thevenin's equivalent resistance. I've been operating under the assumption that to find this value, you simply replace the load with a break, short the voltage sources, break the current sources and calculate the resistance...

However, working some example problems, it seems that gives an incorrect value. Rather, sometimes, to find the equivalent resistance you need to find current through the shorted load and the voltage across the open load... Then of course R=V/I.

It seems from looking over examples I have, the correlation on when to use which method involves having dependent sources. Is this correct? If so, why is this the case?

#### WBahn

Joined Mar 31, 2012
26,139
This is something that really should have been covered fairly carefully by both your text and your instructor.

Let's walk our way up to the answer to your question so that, hopefully, you will fully understand it.

Imagine a general circuit in which you want to find the resistance as seen between a particular set of terminals. Since you are asking about the Thevenin equivalent resistance, I'll assume that you've covered the basic idea that, for a linear circuit (and that's all we are talking about here), you can replace a circuit, however, complicated, with a simple voltage source in series with an equivalent resistance and put your load device in series with that to complete the circuit. In doing so, provided you pick the voltage of the source and the value of the resistance correctly, whatever device or circuit you connect as your load will be unable to tell the difference between the real circuit and the Thevenin equivalent (at least in terms of the voltages and currents at the circuit terminals). The point being that, from the load's perspective, it "thinks" it is connected to a circuit that is to the left of the dashed line in the diagram. Now let's say that you place an adjustable voltage source (Vtest) as your load and set the voltage to 10V (call that V1) and measure the current (Itest) flowing out of it (call that I1) and then increase the voltage to 11V (call that V2) and measure the current again (call that I2).

Let's say that Req turns out to be 1000Ω (1kΩ). We don't know Vth.

Q1) Does knowing just Req give you enough information to find either I1 or I2?

Q2) What can you say, if anything, about the relationship between I1 and I2?

Q3) So, given the answers to Q1 and Q2, what would you say that Req tells you about the circuit?