Which of the following expresses the sinusoidal AC voltage v(t) = 100√2 sin(ωt + π/6) [V] as a phasor (polar form) whose magnitude is the RMS value?

Answer: B. 100∠30° V

Method 1 (from the definition): the magnitude of the phasor is the RMS value, the peak value 100√2 V divided by √2, which is 100 V. The angle is the initial phase π/6 rad = 30°, so the phasor is 100∠30° V. Method 2 (check with complex numbers): 100∠30° = 100(cos 30° + j sin 30°) = 86.6 + j50 V; multiplying by √2 and e^(jωt) and taking the imaginary part gives back the original v(t). In circuit calculations it is usual to use the RMS value, not the peak value, as the magnitude of a phasor.

• A. π/6 rad is 30°, not 60°. Since π rad = 180°, π/6 rad = 180° ÷ 6 = 30°.
• B. Correct. It is the phasor with an RMS value of 100 V and a phase of 30°.
• C. 141 V is the peak value 100√2 V, not the RMS value. Some texts use the peak value as the phasor magnitude, but this question asks for the RMS value.