# Voltage/Current phase diff and more

1. Apr 27, 2009

### martix

Voltage/Current phase difference and more...

Can someone please explain in physical terms what it means that the phase of the voltage lags/leads the current ...among other things...
Like:
1. Impedance - whats the difference between the real and the imag resistance and whats the physical significance of both.
2. The whole reactance idea(general and capacitive/inductive).

Last edited: Apr 27, 2009
2. Apr 29, 2009

### Andrew Mason

Re: Voltage/Current phase difference and more...

A phase difference between voltage and current simply means that points of maximum voltage do not occur at the same time as maximum current.

For a pure capacitor the greatest current occurs when the applied voltage begins to increase from 0 as there is not yet any charge on the capacitor. As the applied voltage increases the charge on the capacitor increases due to the current flow. At the same time, the capacitive reactance (ie. the voltage caused by the charge build up in the capacitor) increases and opposes the applied voltage, thereby limiting current. When the applied voltage is maximum, the applied voltage is the same as the opposing voltage from the build up of charge on the capacitor, so the current is zero. The applied voltage starts to decrease and the charge on the capacitor starts flowing out of the capacitor. The discharge current is maximum when the applied voltage is 0.

So you can see from that qualitative description of a capacitor that current is out of step with voltage. If you plot the sine curve for current and voltage, the current peak will occur 90 degrees (or 1/4 of a cycle) before the voltage peak.

The opposite occurs for an inductor. For an inductor, the voltage peak occurs 90 degrees before current peaks.

AM

Last edited: Apr 29, 2009
3. Apr 29, 2009

### Staff: Mentor

Re: Voltage/Current phase difference and more...

And here's a thread from the EE forum where we discussed this also:

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4. Apr 29, 2009

### Andrew Mason

Re: Voltage/Current phase difference and more...

This is a useful thread. But with respect to this comment:

The terminology might be misleading. In a circuit with a pure inductor or capacitor (R=0) to which an alternating voltage is applied, power is not dissipated. The energy consumed over any number of complete cycles is zero. That is:

$$\int_{0}^{nT} \vec{V}\cdot\vec{I}dt = 0$$

This, of course, ignores loss due to electromagnetic waves, which becomes significant at high frequencies.

A capacitor or inductor does not just absorb energy, it also releases energy. It is the periodic absorption and release of energy that results in no net dissipation of energy.

AM

5. May 1, 2009

### martix

A great explanation from Andrew Mason. Its amazing how the right formulation can put things into perspective. Had a little trouble figuring what happens to an inductor though. As someone mentioned in the other thread - "Most expositions explain the capacitive case but gloss over the inductive one."
As for the real/imag part - I found out about Euler's formula in the mean time. Amazing thing really. :)

Last edited: May 1, 2009