why is the phas angle the same for voltage and resistance in this series cct

eurotrotter

im just windering why the phas angle the same for voltage and resistance in this series cct

thanks guyz
heres the question: its question 3.6



and heres the soulution (question3.6 just a reminder!)

Mad Mike

Do you mean "Why is the angle the same for voltage and impedance (Z) in the line marked (a)"? If so I will try and explain:

The AC version of Ohms law says I=V/Z where I, V and Z are all complex numbers having a magnitude and phase.

If we do this sum in polar notation this means that:
Magnitude (I) = Magnitude(V)/Magnitude(Z)
and Angle(I) = Angle(V)-Angle(Z)
These two equations arise from the rules of complex number arithmetic.

Now remember that in order to assign a phase angle to voltage and currents we need to pick one voltage or current as the reference which we arbitrarily assign a phase of 0. The phase of all other voltages and currents are measured relative to this. You are probably more used to seeing a voltage chosen as the reference. If you choose the voltage as a reference then Angle(V) = 0 and the equation above becomes Angle(I)=-Angle(Z).

However in this solution the person has chosen to make I the reference this means that Angle(I)=0 and when you put this into the equation you get
0=Angle(V)-Angle(Z) or Angle(V)=Angle(Z)

Remember that the choice of reference is entirely arbitrary. It will change the numbers you get for phase angles but only because you are measuring from a different reference. Also the choice of reference doesn't affect the angle of the impedance at all. You could solve thie problem just as easily by choosing voltage as the reference - you may want to try this to test yourself.

eurotrotter

thanks very much for that
but i am still unclear why the phase angle for the current and the resistance are the same

Mad Mike wrote:

Do you mean "Why is the angle the same for voltage and impedance (Z) in the line marked (a)"? If so I will try and explain:

The AC version of Ohms law says I=V/Z where I, V and Z are all complex numbers having a magnitude and phase.

If we do this sum in polar notation this means that:
Magnitude (I) = Magnitude(V)/Magnitude(Z)
and Angle(I) = Angle(V)-Angle(Z)
These two equations arise from the rules of complex number arithmetic.

Now remember that in order to assign a phase angle to voltage and currents we need to pick one voltage or current as the reference which we arbitrarily assign a phase of 0. The phase of all other voltages and currents are measured relative to this. You are probably more used to seeing a voltage chosen as the reference. If you choose the voltage as a reference then Angle(V) = 0 and the equation above becomes Angle(I)=-Angle(Z).

However in this solution the person has chosen to make I the reference this means that Angle(I)=0 and when you put this into the equation you get
0=Angle(V)-Angle(Z) or Angle(V)=Angle(Z)

Remember that the choice of reference is entirely arbitrary. It will change the numbers you get for phase angles but only because you are measuring from a different reference. Also the choice of reference doesn't affect the angle of the impedance at all. You could solve thie problem just as easily by choosing voltage as the reference - you may want to try this to test yourself.

Mad Mike

I don't quite understand your question - could you be more specific please. What line of the solution are you referring to?

If you are asking why the voltage across the resistor has the same angle as the current then that is because a resistor causes no phase shift between voltage and current. The voltage across a resistor is always in phase with the current through the resistor.

Molly

Out of interest, is this Power Engineering in second year of Elec Eng in U.C.C.

eurotrotter

Molly wrote:

Out of interest, is this Power Engineering in second year of Elec Eng in U.C.C.

ya tis!

CathalMc

passattdi110 wrote:

ya tis!

It looked vaguely familiar to me too... small world

SparkyLarks

You decided to make the phase angle of the current 0. so you current is a real number.

V=ZI
AS ther is no imaginary part (reactive component) the phase angle of V and Z must be the same. Multiply an imaginary number by 5 and the phase angle remains the same remember.

If you think of it this way. The phase angle of the voltage is determined by the current passing through an impedance. If the impedance is purely active, the Voltage across the impedance will be active.

If the impedance has a phase angle 90 degrees, purely reactive(inductor). The Voltage across the impedance will lag behind the by 90 degrees.

If the impedance has a phase angle -90 degrees, purely reactive (capacitor). The Voltage across the impedance will lead behind the by 90 degrees.

Ti's the same for all the other phase angles( i.e an inpedance with an activve and reactive component