# network theory

Discussion in 'Homework Help' started by Swag, Apr 12, 2015.

1. ### Swag Thread Starter New Member

Apr 10, 2015
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0
Regarding the statement,

Basically In the sinusoidal case, the power factor is simply cos(θ − φ), where (θ − φ) is the angle by which the voltage leads the current. And in case of an inductor, V leads I by 90° . Then how come the PF for inductive load is said to be lagging?

2. ### Papabravo Expert

Feb 24, 2006
11,071
2,152
I think that is the case for an ideal inductor with no resistance. Also a running motor is an inductive load with a less than ideal power factor.

3. ### WBahn Moderator

Mar 31, 2012
20,057
5,651
You seem to be confusing a couple of concepts.

Leading versus lagging has to do with the relationship of current to voltage in a system. Because we generally supply a voltage and the current is whatever it is, we use the voltage waveform as reference. If we plot the current and the voltage, we will see a shift and if the current reaches a particular point in its waveform (such as the peak or the negative going zero crossing or whatever) before the corresponding point on the voltage waveform, then we say that the current is leading the voltage. If we see that the current reaches that point after the voltage waveform does, then we say that the current is lagging the voltage.

The key is that we always use the voltage as our reference. So if V leads I by 90°, that means that I lags V by 90°.

As for the power factor, note that cos(θ − φ) is the same as cos(φ - θ), so the power factor only depends on the magnitude of the phase difference between voltage and current, not on which is leading or lagging. The power factor itself is positive for both. But we need to distinguish between the case of a less-than-one power factor caused by a capacitive load and that caused by an inductive load because what we do to compensate for each case is very different. So we label the power factor with the same label that describes the relationship of the current to the voltage.