A sinusoidal voltage v 1(t), with 50Hz frequency is represented by a phasor:V1 = -151 + j 42 volts.What is the phase of v 1(t), in radians?Choose a value of radians between - pi and + pi .

A sinusoidal voltage v1(t), with 50Hz frequency is represented by a phasor:

V1 = -151 + j 42 volts.

What is the phase of v1(t), in radians?

The phase of a complex number or phasor is given by the arctangent of the ratio of the imaginary part to the real part. This is also known as the argument of the complex number.

In this case, the phasor V1 is given as -151 + j 42 volts.

The phase φ of V1 is given by:

φ = arctan(Imaginary part / Real part) φ = arctan(42 / -151)

Using a calculator, we find:

φ ≈ arctan(-0.278) ≈ -0.265 radians

However, because the real part of the phasor is negative, we need to adjust the phase by adding π to the result:

φ = -0.265 + π ≈ 2.877 radians

But the question asks for a phase between -π and +π. Therefore, we subtract 2π from the result to bring it into this range:

φ = 2.877 - 2π ≈ -0.265 radians

Therefore, the phase of v1(t) is approximately -0.265 radians.