The superposition theorem for electrical circuits

[Wuberdall]

Hi fellow physicist!

I have some trouble with finding a valid argument, for why the superposition theorem should be fulfilled for electrical circuits - there only containing resistors, capacitors and inductors - where the sources of the emf. are connected in series.

Thanks in advance.

 

[SteamKing]

Have you found any valid arguments why superposition shouldn't be valid for such circuits?

 

[meBigGuy]

Here is a proof. Maybe it will cover the case you are interested in.
http://users.ece.gatech.edu/mleach/papers/superpos.pdf

 

[NascentOxygen]

Hi fellow physicist!

I have some trouble with finding a valid argument, for why the superposition theorem should be fulfilled for electrical circuits - there only containing resistors, capacitors and inductors - where the sources of the emf. are connected in series.

Thanks in advance.

It all hinges on the elements (incl. the sources) being linear over the whole range.

 

[sardar]

The superposition theorem is a fundamental principle in electrical circuits that states that the total voltage or current in a linear circuit is equal to the sum of the individual voltages or currents caused by each source acting separately. This principle is based on the linearity of the circuit components, such as resistors, capacitors, and inductors, which follow Ohm's law and have a proportional relationship between voltage and current.

The reason why the superposition theorem is valid for circuits with only resistors, capacitors, and inductors connected in series is because these components are linear and obey the principle of superposition. This means that the individual effects of each source on the circuit can be calculated separately and then added together to determine the total effect.

Furthermore, the series connection of the sources ensures that the current passing through each component is the same, allowing for the application of Kirchhoff's voltage law to determine the voltage drop across each component. This, in turn, allows for the use of the superposition theorem to calculate the total voltage in the circuit.

In summary, the superposition theorem is valid for electrical circuits with only resistors, capacitors, and inductors connected in series because of the linearity and proportional relationship of these components, and the ability to apply Kirchhoff's voltage law. It is a powerful tool that simplifies the analysis of complex circuits and is essential for understanding and designing electrical systems.