What is a phasor in AC circuit analysis?

What is a phasor in AC circuit analysis?

• A. A real number representing DC amplitude
• B. A complex number representing magnitude and phase of a sinusoid
• C. A vector indicating current direction
• D. A differential operator in AC analysis

Answer: (B)

In AC circuit analysis, a phasor is a complex number that captures both how big a sinusoid is and where its peak occurs in time. For a voltage or current that varies as a sinusoid at a fixed frequency, you can write its phasor as a magnitude with a phase angle, V = |V|∠φ. This lets you work with steady-state signals using simple algebra, because the time dependence can be handled separately: the actual signal is the real part of V e^{jωt}, and derivatives become multiplying by jω in the phasor domain. This makes relationships like I = V/Z easy to handle, since impedance Z links phasors just as resistance links dc quantities. So the phasor really is a complex number that encodes both magnitude and phase of a sinusoid, rather than a real DC value, a direction vector, or a differential operator.

In AC circuit analysis, a phasor is a complex number that captures both how big a sinusoid is and where its peak occurs in time. For a voltage or current that varies as a sinusoid at a fixed frequency, you can write its phasor as a magnitude with a phase angle, V = |V|∠φ. This lets you work with steady-state signals using simple algebra, because the time dependence can be handled separately: the actual signal is the real part of V e^{jωt}, and derivatives become multiplying by jω in the phasor domain. This makes relationships like I = V/Z easy to handle, since impedance Z links phasors just as resistance links dc quantities.

So the phasor really is a complex number that encodes both magnitude and phase of a sinusoid, rather than a real DC value, a direction vector, or a differential operator.