Which statement about phasors is correct for a sinusoidal signal v(t) = Vm cos(ωt + φ)?

Which statement about phasors is correct for a sinusoidal signal v(t) = Vm cos(ωt + φ)?

• A. The phasor magnitude is Vm and angle is φ.
• B. The phasor magnitude is the average value and angle is φ.
• C. Phasors cannot represent cosine signals.
• D. Derivatives in time become division by jω in phasor domain.

Answer: (A)

Phasor representation turns a sinusoid into a rotating complex constant, where its magnitude corresponds to the waveform’s amplitude and its angle corresponds to the phase offset. For v(t) = Vm cos(ωt + φ), the phasor that represents this signal (using peak amplitude) has magnitude Vm and angle φ. This directly matches the time-domain amplitude and phase, since the actual signal is the real part of Vm e^{j(ωt+φ)}. Phasors can represent cosine signals, and time differentiation in the phasor domain becomes multiplication by jω (not division by jω; division would correspond to integration). So the statement that the phasor magnitude is Vm and the angle is φ is the best description.

Phasor representation turns a sinusoid into a rotating complex constant, where its magnitude corresponds to the waveform’s amplitude and its angle corresponds to the phase offset. For v(t) = Vm cos(ωt + φ), the phasor that represents this signal (using peak amplitude) has magnitude Vm and angle φ. This directly matches the time-domain amplitude and phase, since the actual signal is the real part of Vm e^{j(ωt+φ)}. Phasors can represent cosine signals, and time differentiation in the phasor domain becomes multiplication by jω (not division by jω; division would correspond to integration). So the statement that the phasor magnitude is Vm and the angle is φ is the best description.