Simple phase relationship (current & voltage)

[Color_of_Cyan]

Homework Statement

Given tthe following voltage and current


i(t) = 5sin(377t - 20°)A
v(t) = 10cost(377t + 30°)V


Determine phase relationship between i(t) and v(t)

Homework Equations

wave functions

wave properties

The Attempt at a Solution

Would the phase relationship simply be 50° here? Thanks

 

[gneill]

Homework Statement

Given tthe following voltage and current


i(t) = 5sin(377t - 20°)A
v(t) = 10cost(377t + 30°)V


Determine phase relationship between i(t) and v(t)

Homework Equations

wave functions

wave properties

The Attempt at a Solution

Would the phase relationship simply be 50° here? Thanks

Nope. Convert one of the trig functions so that it is the same as the other (for example, convert the cosine to a sine function by applying the appropriate phase shift).

 

[Color_of_Cyan]

So for i(t) would it be

i(t) = 5sin(377t - 20°) = 5cos(377t - 110°) then? It feels like something I should know well already, but it's been years again..

 

[gneill]

So for i(t) would it be

i(t) = 5sin(377t - 20°) = 5cos(377t - 110°) then?

Sure. A phase shift of -90° let's you convert the sin to a cos as you've done. Now you can directly compare the phase shifts between the voltage and current.

It feels like something I should know well already, but it's been years again..

It could be one of those things that you used only once for one homework assignment...

 

[Color_of_Cyan]

So are you just comparing the angles then?

Can you say the difference is simply 140°?

 

[gneill]

So are you just comparing the angles then?

Can you say the difference is simply 140°?

Yes, you want to compare the phase angles when both are based on the same trig function. In this case the phase offset difference is 140°. You might want to investigate further and decide whether the current is leading the voltage by that amount, or lagging it.

 

[Color_of_Cyan]

So how do you tell which is leading which, is it the current always leading the voltage or lagging it ?

I'm thinking the current here may be lagging the voltage by (140° - 90°)

which is by 50° but probably wrong

 

[gneill]

So how do you tell which is leading which, is it the current always leading the voltage or lagging it ?

I'm thinking the current here may be lagging the voltage by (140° - 90°)

which is by 50° but probably wrong

You've already determined that the phase difference between them is 140°. So that's the phase difference.

There is no rule that says the current always leads the voltage. In fact, it can go either way depending upon the components comprising the circuit. Here you've got the time domain expressions for the current and voltage, so you should be able to state which one is leading the other by the phase angles of each when they're both in the same 'sin' or 'cos' form.

Note that when they are in the same form you can add or subtract the same angle from both without changing the relative phase. So, for example, if you had:

i(t) = cos(ωt - 27°)
v(t) = cos(ωt + 134°)

then you could add 27° to both arguments to yield:

i(t) = cos(ωt)
v(t) = cos(ωt + 161°)

leaving the current without a phase angle, and you could then see that v(t) leads i(t) by 161°.

This 'trick' is just for comparing the relative phase angles of two values; don't go using the resulting expressions as the actual time-domain expressions for voltage and current, especially if you have other calculations for voltages and currents elsewhere in the circuit that have their own phases related to the originals.

 

[Color_of_Cyan]

Ah ok thanks, so here the voltage v(t) leads i(t) by 140°.I also take it if something is "leading" by a negative angle it is actually "lagging" instead, right?