Thevenin Equivalent

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:

1. 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.

2. 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.

3. 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. Thus
   

   Analyze 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.

1. Determine the value of R_L that will cause i_b = 0.5 mA.

2. Determine the value of R_L that will cause i_b = 2.5 mA.

3. Determine the value of i_b that will cause R_L = 500 Ohms.

4. 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.