Provide a method to compute the resultant phasor from two sinusoidal voltages with same frequency but different amplitudes and phase angles.

Provide a method to compute the resultant phasor from two sinusoidal voltages with same frequency but different amplitudes and phase angles.

• A. Represent each as phasors and multiply them
• B. Represent V1 ∠θ1 and V2 ∠θ2; convert to rectangular components, sum the real and imaginary parts, then magnitude = sqrt(Re^2 + Im^2) and angle = atan(Im/Re)
• C. Add the magnitudes and angles directly
• D. Subtract the angles only

Answer: (B)

Phasor addition is vector addition in the complex plane. Since the two voltages share the same frequency, you can treat them as phasors and add their vector components, not their magnitudes or angles directly. Write each phasor as V1 ∠θ1 = V1(cosθ1 + j sinθ1) and V2 ∠θ2 = V2(cosθ2 + j sinθ2). Add the rectangular components: Re = V1 cosθ1 + V2 cosθ2, Im = V1 sinθ1 + V2 sinθ2. The resulting phasor is Re + jIm. Its magnitude is Vr = sqrt(Re^2 + Im^2) and its angle is θr = atan2(Im, Re). This gives the resultant phasor Vr ∠θr. If they happen to be in phase (θ1 = θ2), the magnitudes simply add and the angle stays the same. The other approaches—multiplying phasors, directly adding magnitudes and angles, or subtracting angles—don’t reflect the vector nature of phasors and can give incorrect results unless the vectors are aligned.

Phasor addition is vector addition in the complex plane. Since the two voltages share the same frequency, you can treat them as phasors and add their vector components, not their magnitudes or angles directly.

Write each phasor as V1 ∠θ1 = V1(cosθ1 + j sinθ1) and V2 ∠θ2 = V2(cosθ2 + j sinθ2). Add the rectangular components: Re = V1 cosθ1 + V2 cosθ2, Im = V1 sinθ1 + V2 sinθ2. The resulting phasor is Re + jIm. Its magnitude is Vr = sqrt(Re^2 + Im^2) and its angle is θr = atan2(Im, Re). This gives the resultant phasor Vr ∠θr.

If they happen to be in phase (θ1 = θ2), the magnitudes simply add and the angle stays the same. The other approaches—multiplying phasors, directly adding magnitudes and angles, or subtracting angles—don’t reflect the vector nature of phasors and can give incorrect results unless the vectors are aligned.