Alternating current, voltage, sinusoids

[znaya]

Homework Statement

Consider v1 = 30 sin(ωt + 10º) and v2 = 20 cos(ωt - 40º)

A: v1 is in advance to v2
B: v1 differs 50º from v2
C: v2 is in advance to v1
D: v1 is in quadrature to v2

Homework Equations

The Attempt at a Solution

I think the correct answer is A because v1's angle is nearer -∏/2 than v2's.
Does this make any sense?

Thanks for any help.

 

[tiny-tim]

hi znaya!

hint: 20 cos(ωt - 40º) = 20 sin( … ) ?

 

[znaya]

20 cos(ωt - 40º) = 20 sin(ωt + 50º), right?

v1 is in advance, right?

 

[tiny-tim]

20 cos(ωt - 40º) = 20 sin(ωt + 50º), right?

right!

v1 is in advance, right?

i can never remember which way round "in advance" is …

i'll take your word for it! ​

 

[rezeew]

Yes, your answer is correct. In this case, v1 is in advance to v2 because its angle is closer to -π/2 compared to v2's angle. This means that v1 reaches its peak value earlier in time compared to v2. This is because v1 has a phase angle of 10º, which is closer to -π/2 compared to v2's phase angle of -40º. In general, a sinusoidal signal with a smaller phase angle will reach its peak value earlier in time compared to a signal with a larger phase angle.