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Q. 66

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf , three separate wires carry currents for the emfs . 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.

a. Draw a phasor diagram showing phasors for all three phases of a three-phase emf.

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 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.)

c. Show that the potential difference between any two of the phases has the rms value where is the familiar single-phase rms voltage. Evaluate this potential difference for . 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.

(a). Graph is given below.

(b). This means the sum of three phasors is 0

(c).

See the step by step solution

Step by Step Solution

Part (a) Step 1: Given Information

We are given that commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf , three separate wires carry currents for the emfs . 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.

We need to draw the diagram.

Part (a) Step 2: Explanation

the graph of phasors is.

Part (b) Step 1: Given Information

We need to 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 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 (b) Step 2: Explanation

We see the diagram of phasors and we find the sum

In this diagram we see the sum of phasors is

Part (c) Step 1: Given Information

We need to Show that the potential difference between any two of the phases has the rms value , where is the familiar single-phase rms voltage. Evaluate this potential difference for . 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.

Part (c) Step 2: Explanation

From figure we see,

value of difference between phasors

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