How do you know if pf (power factor) is leading or lagging

[pokie_panda]

Homework Statement

power factor leading or lagging

v(t)=3.5cos(600t-120)
i(t)=2.3sin(600t+45)

Homework Equations

pf=cos(Vθ-Iθ)

The Attempt at a Solution

pf=cos(-75)
=.25881905

I get confused, How do we figure out whether it leads or lags.

 

[verty]

Read here: http://en.wikipedia.org/wiki/Leading_and_lagging_current

Then use the phase angles to decide which it is. (This should be correct, I apologize if it isn't.)

 

[NascentOxygen]

I get confused, How do we figure out whether it leads or lags.

You draw the phasor diagram.

The phasors rotate counter-clockwise. Consider a pair rotating together, and differing by an angle ≤ 90°. Whichever passes over an axis first is the leading phasor of that pair.

 

[rude man]

First, change the cos voltage to a sin function. Use sin(x) = cos(x - 90 deg).
Then, you get V = sin(wt + ψ₁) and i = sin(wt + ψ₂).

V leads i if ψ₁ > ψ₂ or ψ₁ - ψ₂ > 0.

 

[rezeew]

As a scientist, we know that power factor (pf) is a measure of the phase difference between voltage and current in an AC circuit. It represents the amount of real power (in watts) that is being used in a circuit, compared to the total power (in volt-amperes) that is being supplied. A power factor of 1 means that all of the supplied power is being used effectively, while a power factor less than 1 indicates that some power is being wasted.

To determine if pf is leading or lagging, we can use the formula pf=cos(Vθ-Iθ), where Vθ is the phase angle of the voltage and Iθ is the phase angle of the current. A positive value for pf indicates a leading power factor, while a negative value indicates a lagging power factor.

In the given example, the voltage function is v(t)=3.5cos(600t-120), which has a phase angle of -120 degrees. The current function is i(t)=2.3sin(600t+45), which has a phase angle of 45 degrees. Substituting these values into the formula, we get pf=cos(-120-45)=cos(-165)=-0.25881905.

Since the value of pf is negative, we can conclude that the power factor in this circuit is lagging. This means that the current is lagging behind the voltage, which can result in wasted power and decreased efficiency. It is important to monitor and correct power factor in electrical systems to ensure optimal performance and energy efficiency.