# How to handle KVL limitations?

In summary: Therefore, the voltage and current in a conductor are zero.So, in summary, the article argues that KVL is not applicable in high frequency AC circuits with changing magnetic fields.
Hi,

I was reading KVL and KCL and I read that KVL cannot be applicable to all the situations specially when :-

" KVL is applicable on the assumption that there is no fluctuating magnetic field linking the closed loop. While, in presence of changing magnetic field in a High Frequency but short wave length AC circuits, the electric field is not a conservative vector field. So, the electric field cannot be the gradient of any potential and the line integral of the electric field around the loop is not zero, directly contradicting KVL. That’s why KVL is not applicable in such a condition "

My Main question is how to deal with this inconsistency or in other words if we face such circuit where AC frequency is high then which method is used
for such kind of circuits to calculate the voltage and current. Many thanks

The PF Insights article https://www.physicsforums.com/insights/circuit-analysis-assumptions/ goes over the assumptions needed for KVL, and KCL, and circuit analysis in general. I think the key one for your question is:

The time scales of interest in CA are much larger than the end-to-end propagation delay of electromagnetic waves in the conductors.

When the frequencies are high enough so that is not true, then you can't use circuit analysis.

Fisherman199 and jim hardy
KVL and KCL are tools applied to "lumped element" circuit analysis. What this means in practice is that you only consider circuit elements that are drawn in the schematic. If magnetic coupling between circuit loops is to be considered, then that should be drawn in the schematics as a circuit element(s), like a transformer between the loops, for example.
Circuit analysis is always an approximation in a purely theoretical sense. Problems often have implicit simplifying assumptions to allow us to use tools like KVL.
So, for example, you probably don't have to worry about quantum mechanics or cosmic rays, unless someone says they matter.

jim hardy
" KVL is applicable on the assumption that there is no fluctuating magnetic field linking the closed loop.

I still regard that claim as 99% sophistry.
Why cannot the induced emf be lumped and represented as just another voltage source?

Antennas , transmission lines and waveguides are a different story .
To me they're a separate field with its own textbooks and math. No place for beginners...

old jim

jim hardy said:
I still regard that claim as 99% sophistry.
Why cannot the induced emf be lumped and represented as just another voltage source?

It might be a semantic difference Jim, but an equivalent circuit is a different circuit. Once you have the equivalent circuit, it is analyzed using CA rules without flux and without charge. An ideal transformer in a transformer equivalent is a device that makes no reference to magnetic flux.

From the article.
The time rate of change of magnetic flux outside any conductor is zero. [##\frac{∂ϕ}{∂t}=0##]
If the initial flux at t=0 was zero, it remains zero. [So basically forget magnetic flux for CA. Forget Poynting vectors.]

The time rate of change of electric charge inside any conductor is zero. [##\frac{∂q}{∂t}=0##]

Fisherman199 and jim hardy

## 1. What is KVL and why is it important to handle its limitations?

KVL stands for Kirchhoff's Voltage Law, which is a fundamental law in circuit analysis that states the sum of voltages around a closed loop in a circuit must equal zero. It is important to handle its limitations because violating KVL can result in incorrect calculations and can lead to circuit malfunction.

## 2. What are the limitations of KVL?

KVL has two main limitations: it assumes ideal circuit conditions and it only applies to closed loops. In real-world circuits, there may be non-ideal elements such as resistors with non-linear characteristics or capacitors with leakage currents. Additionally, KVL cannot be applied to open loops or circuits with multiple sources that cannot be simplified into a single loop.

## 3. How can I handle KVL limitations in my circuit analysis?

One way to handle KVL limitations is to use more advanced circuit analysis techniques such as nodal analysis or superposition, which can account for non-ideal elements and open loops. Another approach is to simplify the circuit by combining multiple sources into a single equivalent source or by using Thevenin or Norton equivalent circuits.

## 4. Is it possible to completely avoid KVL limitations?

No, it is not possible to completely avoid KVL limitations. However, by using more advanced analysis techniques and simplifying the circuit, you can minimize the impact of these limitations on your calculations.

## 5. What are some common mistakes to avoid when handling KVL limitations?

Some common mistakes to avoid when handling KVL limitations include improperly applying KVL to open loops or circuits with multiple sources, neglecting non-ideal elements, and not simplifying the circuit before analysis. It is also important to double-check your calculations and consider the limitations of KVL when interpreting your results.

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