Q.Why is the electric field inside the inductor in RLC circuit zero and why is not zero inside the resistor?Why does Kirchoff's loop's rule does not hold good in RLC circuit?

Please help!!!

From

Suniindra singh

To understand why the electric field inside an inductor in an RLC circuit is zero while it is not zero inside a resistor, we need to delve into the behavior of inductors and resistors in an alternating current (AC) circuit. Additionally, we’ll explore why Kirchhoff's loop rule may not seem to hold in certain situations within RLC circuits.

The Nature of Inductors and Resistors

First, let’s clarify the roles of inductors and resistors:

• Inductor: An inductor stores energy in a magnetic field when current flows through it. The key point is that the electric field inside an ideal inductor is zero because the inductor opposes changes in current. When the current is steady, there’s no electric field generated within the inductor itself.
• Resistor: A resistor, on the other hand, dissipates energy as heat due to the resistance it offers to the flow of electric current. Inside a resistor, there is a non-zero electric field that drives the current through it, according to Ohm's Law (V = IR).

Electric Field in Inductors

In an ideal inductor, when a steady current flows, the magnetic field around the inductor is constant, and thus the induced electric field is zero. This is a result of Faraday's law of electromagnetic induction, which states that a changing magnetic field induces an electric field. If the magnetic field is not changing, there is no induced electric field.

Electric Field in Resistors

In contrast, inside a resistor, the electric field is present because the resistor is designed to convert electrical energy into thermal energy. The electric field within the resistor drives the flow of charge carriers (like electrons) through the material, creating a voltage drop across it. This is why we can measure a voltage across a resistor when current flows through it.

Kirchhoff's Loop Rule in RLC Circuits

Now, let’s address Kirchhoff's loop rule, which states that the sum of the potential differences (voltage) around any closed loop in a circuit must equal zero. In a simple DC circuit, this rule holds true because the voltages across resistors and sources can be easily accounted for. However, in RLC circuits, especially those operating with alternating current, the situation becomes more complex.

Why Kirchhoff's Loop Rule May Seem Invalid

In RLC circuits, particularly under AC conditions, the presence of inductors and capacitors introduces phase differences between voltage and current. This means that the voltages across these components are not necessarily in phase with the current flowing through them. As a result:

• The voltages across inductors and capacitors can lead to a situation where the sum of the voltages does not equal zero when considering instantaneous values.
• When applying Kirchhoff's loop rule, one must account for these phase differences, which can complicate the analysis.

In essence, while Kirchhoff's loop rule still applies, it requires careful consideration of the phase relationships in AC circuits. This often leads to the use of complex numbers and phasors to accurately represent voltages and currents, making the analysis more intricate than in simple DC circuits.

Summary

In summary, the electric field inside an inductor is zero because it opposes changes in current and maintains a steady magnetic field, while the electric field inside a resistor is non-zero due to the resistance it provides to current flow. Kirchhoff's loop rule remains valid in RLC circuits, but the phase differences introduced by inductors and capacitors complicate its application, requiring more advanced techniques for accurate analysis.