Hi

The question is to compute the phase angle and the answer was is arc tan ( V L / V R) according to the diagram on the picture
but how did they find this fornula or the proof of this formula what what phase angle is exactly meant.

 

It's called trigonometry.

Go back to the definition of a phasor.

V·sin(ωt + θ) ⇔ V∠θ

Now consider the addition of two phasors that are 90° out of phase.

V·sin(ωt + θ) = Vr·sin(ωt) + Vl·sin(ωt + 90°)

What are V and θ in terms of Vr and Vl?

 

make sure the phasor is set to stun

 

Hi

The question is to compute the phase angle and the answer was is arc tan ( V L / V R) according to the diagram on the picture
but how did they find this fornula or the proof of this formula what what phase angle is exactly meant.

View attachment 124213

Hi,

Is that diagram and your assumptions about it correct?
I ask because we dont usually see L alone in a formula like that we at least see an 'omega' with it like w*L for example (w=omega), and also V*R/(V*L) simplifies to R/L and V*L/(V*R) to L/R. The 'omega' conveys the frequency information.

For example with R and L in series excited by a voltage V i get for the current phase:
Ph=atan2(-w*L,R)

which you might be able to reduce to:
Ph=-atan(w*L/R)

but we still get the 'w' in there.
Alternately we could do Ph=-atan(xL/R) where xL is the reactance of L at frequency w.


It would be good if you can show the schematic.

 

I'm pretty sure it's not V times L, but V sub L -- i.e., the voltage across the inductor. Similarly, the other phasor is V sub R, the voltage across the resistor. V is then the total voltage of V_L and V_R (which I wrote as Vl and Vr). Since they are being added, the circuit is for a series resistor/inductor branch.

But I agree, a schematic is always nice and would make this a lot clearer.

 

Hi,

Yes i agree that's the most likely way it was done. Thanks for mentioning that.
In that case, we have VR and VL as the two voltages not two multiplications of V times something.

Also in that case, we might check the sign of the phase, but often they dont pay attention to the sign and assume we know if it is lagging or leading based on the component either L or C.