# Drawing Phasor Representation for v(t)=20cos(200t+45°)+cos(200t)

• noppawit
In summary, you are being asked to draw the phasors for each of the cosine waves in v(t) and then add them together to write the equation in the form of a single sinusoid, v(t) = A sin (ωt + φ). This will require converting the time-domain signal into the frequency domain, A∠φ.
noppawit
Draw the phasor representation for each of the following signals. Also write the signal as one sinusoid, v(t) = 20cos(200t+45°)+cos(200t)

From this equation, do I have to turn to v(t) = A sin (ωt + φ) ? If yes, how can I convert it?

Thank you.

I think its asking to first draw the phasors for each one of the cosine waves in v(t). Then add the cosine waves together and write the equation for v(t) as a single sinusoid in the form you listed: A sin (ωt + φ). When drawing the phasors you'll probably want to convert each part of the signal from the time-domain to frequency domain, A∠φ. Hope that helps.

Yes, you can convert the given equation to the form v(t) = Asin(ωt + φ) by using the trigonometric identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b). In this case, A = 20 and ω = 200. To find φ, we can use the fact that cos(45°) = sin(45°) = 1/√2. Therefore, the equation becomes v(t) = 20cos(200t)cos(45°) - 20sin(200t)sin(45°) + cos(200t). Simplifying this, we get v(t) = 10√2cos(200t) - 10√2sin(200t) + cos(200t). Now, we can write this as v(t) = 10√2sin(200t + 45°) + cos(200t). This is now in the form v(t) = Asin(ωt + φ), where A = 10√2, ω = 200, and φ = 45°.

To draw the phasor representation, we can plot a vector with length A = 10√2 at an angle φ = 45° on the complex plane. This represents the first term 10√2sin(200t + 45°). Then, we can plot a vector with length 1 at an angle 0°, representing the second term cos(200t). The resultant phasor representation will be the vector sum of these two vectors, which will have a length and angle determined by the addition of the two individual vectors.

In summary, the phasor representation for v(t) = 20cos(200t+45°)+cos(200t) is a vector with length A = 10√2 at an angle φ = 45° plus a vector with length 1 at an angle 0°. This can also be written as v(t) = 10√2sin(200t + 45°) + cos(200t).

## 1. What is a phasor representation?

A phasor representation is a graphical method used to represent the magnitude and phase of a sinusoidal signal. It is commonly used in electrical engineering and physics to analyze and visualize alternating current (AC) circuits.

## 2. How do you draw a phasor representation for a sinusoidal signal?

To draw a phasor representation, you first need to determine the amplitude, frequency, and phase of the sinusoidal signal. Then, you can use a vector with length equal to the amplitude and angle equal to the phase to represent the signal. The angle is measured counterclockwise from the positive x-axis. Repeat this process for each term in the signal, and the sum of all the phasors will represent the overall signal.

## 3. What do the different components in the phasor representation for v(t)=20cos(200t+45°)+cos(200t) represent?

The amplitude, 20, represents the maximum value of the signal. The frequency, 200, represents the number of cycles per second. The phase, 45°, represents the amount by which the signal is shifted in time. The second term, cos(200t), represents a second sinusoidal signal with the same amplitude and frequency, but with a phase of 0°.

## 4. How can you determine the phase difference between the two sinusoidal signals in the phasor representation?

The phase difference can be determined by finding the angle between the two phasors representing each signal. The difference in angle, measured counterclockwise, represents the phase difference between the two signals. In this case, the phase difference is 45°.

## 5. Can the phasor representation also be used for non-sinusoidal signals?

No, the phasor representation is only applicable to sinusoidal signals. It cannot be used for non-sinusoidal signals, such as square waves or triangle waves, as they do not have a constant amplitude and frequency.

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