Question

In an RL circuit with alternating current, the current lags behind the voltage. What does this mean, and how can it be explained qualitatively, based on the phenomenon of electromagnetic induction?

Short answer

Answer: In an RL circuit with alternating current, the current lags behind the voltage due to the principle of electromagnetic induction and the inductor's magnetic field. When the AC voltage changes, the inductor's magnetic field builds up and collapses while storing and releasing energy, causing resistance to any sudden change in current. As a result, the current changes slower than the applied voltage, and thus, it lags behind the voltage.

Step-by-step solution

1. Overview of RL circuits

An RL circuit is a simple electrical circuit consisting of a resistor (R) and an inductor (L) connected in series, where an alternating current (AC) is applied. In an AC circuit, the voltage and current values change periodically over time. The relationship between voltage and current in an RL circuit can be described by Kirchhoff's voltage law, which states that the sum of potential differences (voltages) around any closed loop in the circuit is equal to zero. In an RL circuit with AC, the voltage across the resistor and inductor will change according to the sinusoidal waveform of the alternating current.

2. Electromagnetic induction

Electromagnetic induction is a phenomenon in which a changing magnetic field induces an electromotive force (EMF) in a conductor. In an inductor, when a current flows through it, it creates a magnetic field around itself. According to Faraday's law of electromagnetic induction, whenever there is a change in the magnetic field within a loop of metal wire, an EMF is induced in the wire that causes a current to flow. In an RL circuit, the inductor acts as a "storehouse" of energy due to the magnetic field created by the flowing current.

3. Current lagging behind voltage in an RL circuit

When an AC voltage is applied to an RL circuit, the sinusoidal waveform causes the current through the inductor to change. When the current in the inductor increases, the magnetic field around it also increases but with a certain time delay as the energy is stored in the magnetic field. When the current decreases, the magnetic field energy is released back into the circuit, again with some delay. This causes the current to lag behind the voltage as the inductor's magnetic field is continuously building up and collapsing in sync with the changing AC voltage.

4. Qualitative explanation based on electromagnetic induction

In an RL circuit, the inductor opposes any sudden change in current because of the principle of electromagnetic induction. When the AC voltage starts to increase, the inductor's magnetic field builds up, resisting the increase in current. Similarly, when the AC voltage begins to decrease, the collapsing magnetic field in the inductor causes an induced EMF, which opposes the decrease in current. As a result, the current through the inductor changes slower than the applied voltage due to the energy being stored and released in the magnetic field. Consequently, the current lags behind the voltage in an RL circuit.