Here is a problem in which it's advantageous to use a Thevenin equivalent circuit. We want to determine the value of R_{L} that will cause i_{b} = 2 mA. (This is problem P5.5-12 from **Introduction to Electric Circuits, 5e** by R.C. Dorf and J.A. Svoboda.) We will solve this problem by finding a Thevenin or Norton equivalent circuit for the part of the circuit that is left of the terminals and then replacing that part of the circuit by its Thevenin or Norton equivalent circuit.

The row of buttons below the circuit correspond to various calculations that are used to find or to use a Thevenin or Norton equivalent circuit.

Thevenin and Norton equivalent circuits involve three parameters:

- V
_{oc}, the open circuit voltage - I
_{sc}, the short circuit current - R
_{th}, the Thevenin Resistance

The buttons labeled "Voc", "Isc" and "Rth" show how to find a Thevenin or Norton equivalent circuit for the part of the circuit that is left of the terminals:

- Left-click on the "Voc" button to see the circuit used to determine V
_{oc}, the open circuit voltage. The voltmeter measures the value of V_{oc}in volts. Analyze this circuit, e.g. by writing and solving a mesh equation, to verify the value of V_{oc}. - Left-click on the "Isc" button to see the circuit used to determine I
_{sc}, the short circuit current. The ammeter measures the value of I_{sc}in mA. Analyze this circuit, e.g. by writing and solving a mesh equation, to verify the value of I_{sc}. - Left-click on the "Rth" button to see the circuit used to determine R
_{th}, the Thevenin Resistance. The current source causes the current in the equivalent resistance to be 1 mA. The voltmeter measures the value of the voltage across the equivalent resistance in volts. ThusAnalyze this circuit, e.g. by writing and solving a mesh equation, to verify the value of R

_{th}.

As expected (Section 5.5 of **Introduction to Electric Circuits** by RC Dorf and JA Svoboda), V_{oc}, I_{sc} and R_{th} are related by

The buttons labeled "Thevenin" and "Norton" show the circuits that result when the part of the circuit that is left of the terminals is replaced by its Thevenin or Norton equivalent circuit.

Left-click on the "Thevenin" button to see the circuit that we get when we use the Thevenin equivalent circuit. Analysis of this circuit shows

Next, left-click on the "Norton" button to see the circuit that we get when we use the Norton equivalent circuit. Analysis of this circuit shows

Of course, we expect both of these calculations to yield the same value of R_{L}.

Finally, left-click on the "circuit" button to return to the original circuit. Verify that setting R_{L} = 0 does indeed cause i_{b}=2 mA.

- Determine the value of R
_{L}that will cause i_{b}= 0.5 mA. - Determine the value of R
_{L}that will cause i_{b}= 2.5 mA. - Determine the value of i
_{b}that will cause R_{L}= 500 Ohms. - Here is a version of this example that includes scrollbars. Use the scrollbars to change the parameters of the part of the circuit that is left of the terminals. Rework this example after changing the circuit parameters.