Question

Find the standard sinusoidal representation of the given phasor. Express all as positive quantities, with phase from 0 to 359 degrees. v= 20⁻²⁷⁰° ω=30

v (t) =_____cos(____t+____°)

Answer 1

The standard sinusoidal representation of the given phasor with an amplitude of 20 and a phase angle of -270 degrees (equivalent to +90 degrees) with an angular frequency of 30 radians per second is v(t) = 20 cos(30t + 90°).

Step-by-step explanation:

To find the standard sinusoidal representation of the given phasor expressed as positive quantities and with phase from 0 to 359 degrees, we should first note that a phasor in the form v = 20⁻²⁷° suggests an amplitude of 20 units and a phase angle of -270°, which is equivalent to +90° (since -270° + 360° = 90°).

The sinusoidal function associated with a phasor can be represented by either a sine or a cosine function. Given the angular frequency ω which is 30 radians per second, we will use the cosine function for this representation. Therefore, the given phasor can be represented in the form:

v (t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency (also known as the angular velocity), and φ is the phase angle.

v (t) = 20 cos(30t + 90°)

We have expressed the phasor as a cosine function with an amplitude of 20, an angular frequency of 30 radians per second, and a phase angle of 90 degrees.