Useful information | 8 animated pictures to understand the lead and lag of voltage and current in seconds
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Since Sin[ωt] will become Sin[ωt±90°] after differentiation or integration, for inductors and capacitors connected to a sine wave, the phenomenon of waveform lead and lag can be observed when the horizontal axis is ωt. It is not easy to understand directly from a static function graph, so it is better to make an animation.
The figure below is of an inductor, with voltage represented by red and current represented by blue.
If an ideal DC voltmeter and DC ammeter are connected, it can be observed that the change in voltage leads the change in current, and the change in current lags behind the voltage.
As time increases, the vertical axis and the time origin will move to the left along with the waveform.
If the waveform is drawn on the right side of the vector diagram, it will be the animation below, but the waveform on the right side of the horizontal axis is the waveform that existed in the past, pointing to the past, which is -ωt.
Although the waveform is reversed, the change in voltage still leads the change in current, and the change in current still lags behind the voltage.
The time origin has been moving to the right with the waveform. The vertical axis in the function graph does not intersect the horizontal axis at the origin, and the time represented by the intersection has been increasing.
If you are not careful, it is easy to make mistakes in judging lead or lag.
The best way to understand the concept of lead-lag is to use a phasor diagram. Observing from measured data or static waveforms is not very intuitive and is prone to errors.
The following figure is a capacitor. The change in voltage lags behind the current, and the change in current leads the voltage. The right side of the coordinate system is the future, and the left side is the past.
When the horizontal axis is -ωt, the change of the capacitor voltage still lags behind the current, and the change of the current still leads the voltage.
Because the left side of this coordinate system is the future and the right side is the past.
The figure below is for a resistor. The voltage function and the current function are in phase.
The total voltage is not drawn because the total voltage may be ahead of the total current, it may lag behind the total current, or it may be in phase with the total current. When they are in phase, it is a resonant state.
However, when it comes to explaining the concept of lead-lag, the animation of the pointer meter is more intuitive.
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