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be sure to use emf_rms in your answer for part C and not emf_rm as directed by t

ID: 1263466 • Letter: B

Question

be sure to use emf_rms in your answer for part C and not emf_rm as directed by the problem.

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf Epsilon = Epsilon 0 cos wt, three separate wires carry currents for the emfs Epsilon 1 = Epsilon 0 cos wt, Epsilon 2 = Epsilon 0 cos(wt + 120 degree), and Epsilon 3 = Epsilon 0 cos(wt - 120 degree). 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. Part B Show that the sum of the three phases is zero, producing what is referred to as neutral. In single-phase electricity, provided by the familiar 120 V/60 Hz electric outlets in your home, one side of the outlet is neutral, as established at a nearby electrical substation. The other, called the hot side, is one of the three phases. (The round opening is connected to ground.) Part C Find an expression for the rms value of the potential difference between any two of the phases. Assume that epsilon rms is the familiar single-phase rms voltage. 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.

Explanation / Answer

PARTB)

transmission lines are 3 phase type

they are designated as R Y B

line will be balanced only when phasor sum of all three lines equal to zero

it has to satisfy that they should have same frequency

I=IR+IY+IB

=Ecos(wt)+Ecos(wt-120)+Ecos(wt+120)

=Ecos(wt)+Ecos(wt)*0.866-Esin(wt)*0.5-Ecos(wt)*0.866+Esin(wt)*0.5

=0

PARTC)

transmissionlines are starconnected

phase voltage=line voltage/sqrt(3)

vline=Ecos(wt)-Ecos(wt-120)

=sqrt(3)*phasevoltage