# How to write a voltage in phasor form (using a reference-voltage)

I have the following problem:
Consider two voltages described by

v1 = 325 sin(wt+10º) V
v2 = 326 sin(wt+130º) V

Write v2 in Phasor Form using v1 as reference...

My Question is:
I understand that the angle will be 120º, but what will the voltage be?
Below is a drawing of how I am imagining it to be from a trigonometric point of view, but maybe this is the wrong way to look at the problem?

• Draw a diagram and you'll see that you can work it out from trigonometry. Be careful with the angle. It's relative to V1. – Transistor Jan 22 at 12:13
• @Transistor , thanks for the answer, but I am still confused on how I should go about to solve the problem, could you please give me some more guidance?:) – August Jelemson Jan 22 at 12:29
• Draw the diagram and edit a sharp, cropped photo into your question. Show 0, V1, V2 and the phasor from V1 to V2. – Transistor Jan 22 at 12:31
• @Transistor , hi again, I have thought a little bit more about what you said, and I have updated the question, would you mind take a look?:) – August Jelemson Jan 22 at 15:00
• V1=325∠0 and V2=326∠120 but remember that ∠0 is used as reference for $$\omega t +10$$ so frequency is also important you cannot add two voltage of different frequencies using phasors! – user215805 Jan 22 at 15:19

To find it without drawing phasors you just add/subtract $$\\theta °\$$ to/from all of your phasors where $$\\theta °\$$ is the angle that when added/subtracted from your reference phasor will make it $$\0°\$$. In your case you can subtract $$\10°\$$ from each phasor (thus making $$\v_1\$$ your reference).
Making $$\v_1\$$ the reference means you adjust its angle to $$\0°\$$. When you do this, the entire phasor diagram rotates with $$\v_1\$$ until $$\v_1\$$ is at the $$\0°\$$ position.
For example, below on the left are two arbitrary phasors $$\V_X\$$ and $$\V_Y\$$. On the right I have made $$\V_X\$$ the reference and put it at position $$\0°\$$.
What really matters with phasors is their position relative to each other. Rotating the whole group around does not change their relationship to each other. Further, you can use whatever angle you want as the reference. Some folks use $$\90°\$$ so it is whatever you prefer.