Final answer:
Given the phasor voltage and current with their respective angles, the phase difference between voltage and current indicates that the element is an inductor, since the current lags the voltage by 90°.
Step-by-step explanation:
To determine the nature of an element given a phasor voltage of V = 200< 30°V and a phasor current of I = 2<120°A, we examine the phase difference between the voltage and current. If the current leads the voltage, the element is a capacitance; if the current lags the voltage, it is an inductance; and if they are in phase, it is a resistance.
We can calculate the phase difference (δ) as follows:
δ = θv - θi
δ = 30° - 120°
δ = -90°
A negative phase difference indicates that the current lags the voltage by 90°, which is characteristic of an inductive element. Hence, the element is an inductor.
No additional information about the angular frequency is required to determine the nature of the element in this case. However, note that the angular frequency would be relevant when calculating the actual inductive reactance of the inductor if that were needed.