Exploring EMF and Faraday's Law in LR Circuits

In summary, Kirchoff's voltage law works when analyzing non-steady circuits because the circuit follows three assumptions, including no net charge on any component, no magnetic flux outside any component, and a small enough circuit for the speed of light to be considered instantaneous. These assumptions reduce Maxwell's equations to Kirchoff's laws, making them an accurate method for analyzing non-steady circuits.
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Lost1ne
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1) Take a non-steady circuit such as an LR circuit. Why does Kirchoff's voltage law work when analyzing such a circuit? Is it because we're assuming that dI/dt and thus dB/dt are approximately zero thus meaning that curl E is approximately zero?
2) ε, the electromotive force, is the line integral of the force per unit charge integrated around a circuit. Although I feel many texts don't make this distinction clear (maybe because it's trivial), this is not necessarily equal to -dΦ/dt, Φ being the magnetic flux through our designated surface following Faraday's Law, correct? If so, we would already have a clear contradiction using an example like a steady circuit consisting of a battery and a resistor. -dΦ/dt is only the induced EMF, and this adds algebraically with a pre-existing EMF, right? In the end, the net EMF must follow the line integral definition.
 
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Lost1ne said:
Take a non-steady circuit such as an LR circuit. Why does Kirchoff's voltage law work when analyzing such a circuit?
Circuit theory is based on three assumptions. The first is that there is no net charge on any component. The second is that there is no magnetic flux outside any component. The third is that the circuit is small enough that the speed of light can be considered to be instantaneous.

With those three assumptions Maxwell’s equations reduce to Kirchoff’s laws. So the reason that Kirchoff’s laws work for a R.L. Circuit is simply that the circuit obeys those assumptions to a very good approximation.
 
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Related to Exploring EMF and Faraday's Law in LR Circuits

1. What is EMF and how does it relate to LR circuits?

EMF stands for electromotive force, and it is the force that drives the flow of electric current in a circuit. In LR circuits, EMF is generated by the changing magnetic field due to the inductance of the circuit.

2. What is Faraday's Law and how does it apply to LR circuits?

Faraday's Law states that a changing magnetic field will induce an electric field, which in turn will produce an EMF. In LR circuits, Faraday's Law explains how the changing magnetic field due to the inductance of the circuit creates an EMF.

3. How do you calculate the EMF in an LR circuit?

The EMF in an LR circuit can be calculated using the formula EMF = -L(dI/dt), where L is the inductance of the circuit and dI/dt is the rate of change of current. This formula is derived from Faraday's Law.

4. What is the purpose of exploring EMF and Faraday's Law in LR circuits?

Exploring EMF and Faraday's Law in LR circuits allows us to understand the relationship between electricity and magnetism, and how they interact to produce electric currents. This knowledge is crucial in designing and analyzing various electronic devices and systems.

5. How does the resistance affect the EMF in an LR circuit?

The resistance in an LR circuit affects the EMF by creating a voltage drop, which opposes the EMF. This is known as the voltage drop across the resistor. The higher the resistance, the greater the voltage drop and the lower the EMF in the circuit.

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