- #1
rudy
- 45
- 9
- Homework Statement
- Find the phasor which corresponds to v(t), which is the sum of two waveforms:
v(t) = 2cos(8t+180) + 10cos(8t+30) volts
find phasor "V" for the above waveform
phase angles are given in degrees
answers are to be given in radians for exp. form, or rectangular form.
- Relevant Equations
- r ∠⦵ = r*e^(i*⦵) (polar to exponential notation)
rcos(wt+⦵) = r∠⦵
basic trig formulas, vector addition
v(t) = 2cos(8t+180) + 10cos(8t+30) volts
polar form
= 2∠180 + 10∠30
convert to rectangular to add vectors
= (2cos180 + i*2sin180) + (10cos30 + i*10sin30)
= (-2 + i*0) + (8.66 + i*5) = 6.66 + i*5
find ⦵ and r of sum of vectors
⦵ = arctan(5/6.66) = 0.64
r = sqrt(5^2 + 6.66^2) = 8.33
V = 8.33*e^(i*0.64) ("incorrect answer")
note: I successfully answered another phasor question using this exact entry format. For this question I have tried entering the phasor in exponential (radians and degrees just to check) as well as rectangular.
For a previous question I was graded incorrect for not using the constant "pi" in my answer, could I be missing something like that here or is there a problem with my calculation?
polar form
= 2∠180 + 10∠30
convert to rectangular to add vectors
= (2cos180 + i*2sin180) + (10cos30 + i*10sin30)
= (-2 + i*0) + (8.66 + i*5) = 6.66 + i*5
find ⦵ and r of sum of vectors
⦵ = arctan(5/6.66) = 0.64
r = sqrt(5^2 + 6.66^2) = 8.33
V = 8.33*e^(i*0.64) ("incorrect answer")
note: I successfully answered another phasor question using this exact entry format. For this question I have tried entering the phasor in exponential (radians and degrees just to check) as well as rectangular.
For a previous question I was graded incorrect for not using the constant "pi" in my answer, could I be missing something like that here or is there a problem with my calculation?
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