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In alternating current, we may have inductors and capacitors which make voltage and current become out of sync.

enter image description here

At the beginning, I was stuck because how can it be that there is first voltage and then current? Now I realized that it's not the current or the voltage itself what is going before or after the other.

It's the way the values increase and decrease what is out of sync.

Both voltage and current start simultaneously existing at the exact same time, but their values increase, decrease and are zero at different times.

That has clarified my ideas a lot, but I am struggling to visualize what is really going on in each case.

I think this can be broken down to:

  • The effect of voltage being greater than current.
  • The effect of voltage being lower than current.
  • The effect of having whatever voltage and zero current.
  • The effect of having zero voltage and whatever current.

Apart to those facts, there is also a need to deal with what happens with positive and negative values, which could be broken down to:

  • The effect of having opposite voltage and current.
  • The effect of having same-direction voltage and current.

Could anyone please provide some analogies or simplified views where the effect of this can be understood?

Of course analogies might not be 100% accurate or might oversimplify stuff, but it's better to have a simple understanding than none. Which means: whatever coherent insight will be highly appreciated.

For the sake of not making this a lazy question, I will explain what my intuition tells me:

The effect of voltage being greater than current:

High voltage and low current means that some force is pushing the current back. It could also be that there is only a small amount of charge available in the circuit.

The effect of voltage being lower than current:

Low voltage and high current means that there is an extra force helping the current to flow faster.

The effect of having whatever voltage and zero current:

I cannot understand this. The only way for this to happen is to have a barrier that does not allow charge carriers to cross that barrier.

The effect of having zero voltage and whatever current:

Current does not have any motivation to flow if there is no voltage. This could only happen if there is some kind of inertia.

The effect of having opposite voltage and current:

This is even crazier. Voltage pushes the charges from A to B, but they just decide to go from B to A. Something must be causing this reverse behaviour.

The effect of having same-direction voltage and current:

This seems to be very normal.

Oversimplified conclusion:

My brain explodes when I try to put all of this together.

But this is what it understands (can you please correct the wrong affirmations?):

Voltage is what is actually being created at the source (for example a magnet that goes in and out of a coil).

Current flow is the consequence of voltage (And never viceversa).

The fact that the magnet smoothly goes in and out explains the sinusoidal form of AC.

Smoothly in from -max to max, stop, smoothly out from max to -max.

In a simple circuit with a resistance, both voltage and current would go together.

If I introduce a capacitor, with the capacity of storing the charges... it "steals" the current for a while, until it just stops "stealing" (= is full). That would make the current disappear or stop at some point, but it does not apparently relate to the waves shown above.

If I introduce an inductor, with the behaviour of stopping the charges flow until a magnetic field is created... it "pushes back" the charges until they just keep going on. That would make the current and voltage sync back at some point, but it does not apparently relate to the waves shown above.

If I introduce both a capacitor and an inductor, it could be broken down to having only one of both. The one that is "bigger" wins. And its behaviour could be understood by understanding the previous ones.

This is a broad question, but I feel this is the only way I can ask, since that is the big picture and it makes no sense to break it down into many small separated questions.

Thanks for your attention.

Image source: wikiwand.com

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  • $\begingroup$ By "tension" do you mean "voltage" ? $\endgroup$ Dec 14, 2019 at 11:31
  • $\begingroup$ @aditya_stack Yes, I will update the question and change the word. $\endgroup$ Dec 14, 2019 at 11:32

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Rather than try and respond to each of your comments one at a time, I will attempt to give you both a mathematical and physical explanation of the waveforms. If this explanation does not answer a specific point of yours, let me know by comment(s).

CAPACITOR:

Mathematical Explanation:

The basic relationship between current and voltage for a capacitor is

$$i(t)=C\frac{dv(t)}{dt}$$

In your diagram, the voltage is a sine wave. The derivative of the sine is the cosine, which is your current waveform.

Physical Explanation:

The previous equation can be rewritten:

$$v(t)=\frac{1}{C}\int_0^t i(t)dt$$

Where the initial voltage across the capacitor is zero.

The relationship between voltage, charge and capacitance is

$$V=\frac{Q}{C}$$

Since current is the rate of delivery of charge to the capacitor, the integral tells us it takes time to deliver that charge to the capacitor which in turn means it takes time for voltage to build on the capacitor. It is therefore said you can't change the voltage across an ideal capacitor instantaneously (i.e., in zero time). So while we initially have current at t=0 we have no voltage at t=0.

As time passes the voltage builds on the capacitor. When it does it reduces the current delivered by the source. That's why the current is decreasing while the voltage across the capacitor is increasing. When the voltage reaches a maximum, the current is zero. Now the current reverses direction, which means charge is now coming off the capacitor. That reduces the voltage across the capacitor. When the voltage is zero, the current is a maximum negative value.

INDUCTOR:

Mathematical Explanation:

The basic relationship between current and voltage for an inductor is

$$v(t)=L\frac{di(t)}{dt}$$

In your diagram, the current is a cosine. The derivative of the cosine is the minus sine, which is your voltage waveform.

Physical Explanation:

The previous equation can be rewritten:

$$i(t)=\frac{1}{L}\int_0^t v(t)dt$$

Where the initial current in the inductor is zero.

The integral tells us that it takes time for the current to change in an inductor, or to put it another way, you can't change the current in an ideal inductor instantaneously (in zero time). For this reason it is said that the voltage leads the current (or current lags the voltage) in an inductor. The voltage (emf) induced in an inductor resists a change in current. As time passes the current increases and the voltage decreases. The current is a maximum or minimum when the voltage is zero.

Hope this helps.

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  • $\begingroup$ This is a wonderful explanation, thank you very much. $\endgroup$ Dec 14, 2019 at 14:35
  • $\begingroup$ @AlvaroFranz You are very welcome $\endgroup$
    – Bob D
    Dec 14, 2019 at 14:47

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