Thevenin And Maximum Power Transfer

Sample Solution

Yes, Thevenin's theorem is applicable to both AC and DC circuits. The only difference is that in AC circuits, the Thevenin equivalent voltage and impedance are complex numbers.

Source Transformation vs. Superposition for Finding the Thevenin Equivalent Voltage

Both source transformation and superposition can be used to find the Thevenin equivalent voltage of a circuit. However, source transformation is generally easier to use for circuits with a single voltage source, while superposition is generally easier to use for circuits with multiple voltage sources.

Full Answer Section

Source Transformation Solution

To find the Thevenin equivalent voltage using source transformation, follow these steps:

1. Identify the load resistor. This is the resistor that you are interested in finding the Thevenin equivalent voltage across.
2. Disconnect the load resistor.
3. Transform all of the voltage sources in the circuit into current sources. To do this, divide each voltage source by its series resistance.
4. Combine all of the current sources in the circuit into a single equivalent current source.
5. Reconnect the load resistor.
6. Calculate the voltage across the load resistor. This is the Thevenin equivalent voltage.

Superposition Solution

To find the Thevenin equivalent voltage using superposition, follow these steps:

1. Identify the voltage sources in the circuit.
2. Turn off all of the voltage sources except for one.
3. Calculate the voltage across the load resistor due to the remaining voltage source.
4. Repeat steps 2 and 3 for each voltage source in the circuit.
5. Sum the voltages from each step to find the total voltage across the load resistor. This is the Thevenin equivalent voltage.

Example

Consider the following circuit:

Opens in a new windowelectronics.stackexchange.com

circuit with two voltage sources and a load resistor

To find the Thevenin equivalent voltage using source transformation, we would follow these steps:

1. Identify the load resistor. The load resistor is the 10 Ω resistor.
2. Disconnect the load resistor.
3. Transform all of the voltage sources into current sources. The 12 V voltage source can be transformed into a 1 A current source, and the 6 V voltage source can be transformed into a 0.6 A current source.
4. Combine all of the current sources into a single equivalent current source. The equivalent current source is 1.6 A.
5. Reconnect the load resistor.
6. Calculate the voltage across the load resistor. The voltage across the load resistor is 16 V.

To find the Thevenin equivalent voltage using superposition, we would follow these steps:

1. Identify the voltage sources in the circuit. The voltage sources are the 12 V voltage source and the 6 V voltage source.
2. Turn off all of the voltage sources except for one. Turn off the 6 V voltage source.
3. Calculate the voltage across the load resistor due to the remaining voltage source. The voltage across the load resistor due to the 12 V voltage source is 12 V.
4. Repeat steps 2 and 3 for each voltage source in the circuit. Turn on the 6 V voltage source and turn off the 12 V voltage source. The voltage across the load resistor due to the 6 V voltage source is 6 V.
5. Sum the voltages from each step to find the total voltage across the load resistor. The total voltage across the load resistor is 18 V.

Conclusion

Both source transformation and superposition can be used to find the Thevenin equivalent voltage of a circuit. However, source transformation is generally easier to use for circuits with a single voltage source, while superposition is generally easier to use for circuits with multiple voltage sources.

In my opinion, source transformation is the easier method to use for the circuit in the example. This is because the circuit only has a single voltage source.