31. Alternating Current

Which of the following best describes the relationship between three voltages $V_1$, $V_2$, and $V_3$ in a phasor diagram if $V_1$ and $V_2$ are out of phase and their sum gives $V_3$?

The following phasor diagram shows an arbitrary phasor during its first rotation. Assuming that it begins with an angle of 0° , if the phasor took 0.027 s to get to its current position, what is the angular frequency of the phasor?

An AC source oscillates with an angular frequency of 120 s^-1 . If the initial voltage phasor is shown in the following phasor diagram, draw the voltage phasor after 0.01 s. (Select the correct absolute angle below of the phasor's location below after you have drawn it.)

A phasor of length 4 begins at 0° . If it is rotating at ω = 250 s⁻¹ , what is the value of the phasor after 0.007 s?

The emf phasor in FIGURE EX32.1 is shown at t = 2.0 ms. What is the angular frequency ω? Assume this is the first rotation.

The emf phasor in FIGURE EX32.1 is shown at t = 2.0 ms. What is the peak value of the emf?

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf ε = ε₀ cos ωt, three separate wires carry currents for the emfs ε₁ = ε₀ cos ωt, ε₂ = ε₀ cos(ωt+120°), and ε₃ = ε₀ cos(ωt−120°). This is why the long-distance transmission lines you see in the countryside have three parallel wires, as do many distribution lines within a city. Show that the potential difference between any two of the phases has the rms value 3–√ ε_rms, where ε_rms is the familiar single-phase rms voltage. Evaluate this potential difference for ε_rms = 120 V. Some high-power home appliances, especially electric clothes dryers and hot-water heaters, are designed to operate between two of the phases rather than between one phase and neutral. Heavy-duty industrial motors are designed to operate from all three phases, but full three-phase power is rare in residential or office use.