CE Trainee said:The Attempt at a Solution
x1 in rectangular form = 7.07 + j7.07
x2 in rectangular form = -7.07 + j7.07
x3 = x1 + x2 = 0 + j14.14
x3 magnitude = 14.14
x3 phase = arctan( 14.14 / 0 )?
A phasor is a complex number used to represent a sinusoidal function in the frequency domain. It has a magnitude and a phase angle, which represent the amplitude and phase of the sinusoid, respectively.
In some circuits or systems, there may be equal and opposite real components that cancel out each other. For example, in an RLC circuit, the reactive components (inductance and capacitance) can cancel out the resistance, resulting in a purely imaginary impedance.
To find the sum of phasors when the real components cancel out, you can use the Pythagorean theorem. First, square the magnitudes of the phasors, then add them together. Finally, take the square root of the sum to find the magnitude of the resulting phasor. The phase angle of the resulting phasor can be found using trigonometric functions.
Finding the sum of phasors can help in analyzing and solving complex circuits or systems. When the real components cancel out, it means that the system has a purely reactive impedance, which can affect the behavior of the system. By finding the sum of phasors, we can determine the overall impedance and phase angle of the system.
No, the sum of phasors will always result in a positive magnitude, as it is the square root of the sum of squared magnitudes. However, the phase angle of the resulting phasor can be positive or negative, depending on the direction of the phasors in the complex plane.