In AC circuits, phasor representation expresses sinusoidal quantities as complex numbers using magnitude and phase. Which statement is true?

In AC circuits, phasor representation expresses sinusoidal quantities as complex numbers using magnitude and phase. Which statement is true?

• A. A phasor uses only magnitude and ignores phase.
• B. A phasor represents sinusoidal quantities as complex numbers using magnitude and phase.
• C. Phasors are time-domain functions with real numbers only.
• D. Phasors cannot be used to represent impedances.

Answer: (B)

Phasors turn a time-varying sinusoid into a complex number that carries both its magnitude and its phase. If a voltage or current is v(t) = Vm cos(ωt + φ), the corresponding phasor is V = Vm ∠ φ (or Vm e^{jφ}). The real time signal is recovered by taking the real part of V e^{jωt}, so the phasor keeps track of how large the signal is and where it’s located in its cycle. This representation makes circuit analysis easier because differentiation and integration with respect to time become simple algebra for phasors. Ohm’s law in the phasor domain is V = I Z, with Z being the complex impedance R + jX. The real part R shows resistance, while the imaginary part X (positive for inductors, negative for capacitors) captures how voltages and currents shift in time relative to each other. The phase information is essential; it’s what lets us describe constructive or destructive timing between voltages and currents. So the statement that phasors represent sinusoidal quantities as complex numbers using magnitude and phase is correct. The other options misstate the role of phase, imply time-domain real-valued functions, or deny that impedances can be represented in this framework.

Phasors turn a time-varying sinusoid into a complex number that carries both its magnitude and its phase. If a voltage or current is v(t) = Vm cos(ωt + φ), the corresponding phasor is V = Vm ∠ φ (or Vm e^{jφ}). The real time signal is recovered by taking the real part of V e^{jωt}, so the phasor keeps track of how large the signal is and where it’s located in its cycle.

This representation makes circuit analysis easier because differentiation and integration with respect to time become simple algebra for phasors. Ohm’s law in the phasor domain is V = I Z, with Z being the complex impedance R + jX. The real part R shows resistance, while the imaginary part X (positive for inductors, negative for capacitors) captures how voltages and currents shift in time relative to each other. The phase information is essential; it’s what lets us describe constructive or destructive timing between voltages and currents.

So the statement that phasors represent sinusoidal quantities as complex numbers using magnitude and phase is correct. The other options misstate the role of phase, imply time-domain real-valued functions, or deny that impedances can be represented in this framework.