1.7 Applications2

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1.7 Applications2

In this section, we will consider tw o practical applications of the con cepts developed in this chapter. The first one deals with the TV picture tube and the other with how electric utilities determine your electric bill.

1.7.1 TV Picture Tube

One important application of the motion of electrons is found in both the transmission and reception of TV signals. At the transmission end, a TV camera reduces a scene from an optical image to an electrical signal. Scanning is accomplished with a thin beam of electrons in an iconoscope camera tube.

At the receiving end, the image is reconstructed by using a cathoderay tube (CR T) located in the TV recei ver.3 The CRT is depicted in Fig. 1.17. Unlike the iconoscope tube, which produces an electron beam of constant intensity, the CRT beam varies in intensity according to the incoming signal. The electron gun, maintained at a high potential, fires the electron beam. The beam passes through two sets of plates for vertical and horizontal deflections so that the spot on the screen where the beam strikes can move right and left and up and down. When the electron beam strikes the fluorescent screen, it gives off light at that spot. Thus, the beam can be made to “paint” a picture on the TV screen.

² The dagger sign preceding a section heading indicates the section that may be skipped, explained briefly, or assigned as homework.

³ Modern TV tubes use a different technology.

Cathode-ray tube.

Historical

Karl Ferdinand Braun and Vladimir K. Zworykin

Karl Ferdinand Braun (1850–1918), of the University of Strasbourg, invented the Braun cathode-ray tube in 1879. This then became the basis for the picture tube used for so many years for televisions. It is still the most economical device today, although the price of flat-screen systems is rapidly becoming competitive. Before the Braun tube could be used in television, it took the inventiveness of Vladimir K. Zworykin (1889–1982) to develop the iconoscope so that the modern television would become a reality. The iconoscope developed into the orthicon and the image orthicon, which allowed images to be captured and converted into signals that could be sent to the television receiver. Thus, the television camera was born.

The electron beam in a TV picture tube carries 10 Example 1.8 15 electrons per second. As a design engineer, determine the voltage Vo needed to accelerate the electron beam to achieve 4 W.

Solution:

The charge on an electron is

e = −1.6 × 10⁻19 C

If the number of electrons is n, then q = ne and

$$i = \frac{dq}{dt} = e \frac{dn}{dt} = (-1.6 \times 10^{-19})(10^{15}) = -1.6 \times 10^{-4} \text{ A}$$

The negative sign indicates that the current flows in a direction opposite to electron flow as shown in Fig. 1.18, which is a simplified diagram of the CRT for the case when the vertical deflection plates carry no charge. The beam power is

$$p = V_o i$$

or $V_o = \frac{p}{i} = \frac{4}{1.6 \times 10^{-4}} = 25,000 \text{ V}$

Thus, the required voltage is 25 kV.

Practice Problem 1.8

If an electron beam in a TV picture tube carries 10 13 electrons/second and is passing through plates maintained at a potential difference of 30 kV, calculate the power in the beam.

Answer: 48 mW.

1.7.2 Electricity Bills

The second application deals with ho w an electric utility compan y charges their customers. The cost of electricity depends upon the amount of ener gy consumed in kilo watt-hours (kWh). (Other f actors that affect the cost include demand and po wer factors; we will ignore these for now.) However, even if a consumer uses no energy at all, there is a minimum service char ge the customer must pay because it costs money to stay connected to the po wer line. As ener gy consumption increases, the cost per kWh drops. It is interesting to note the a verage monthly consumption of household appliances for a family of five, shown in Table 1.3.

TABLE 1.3

Typical average monthly consumption of household appliances.

Appliance	kWh consumed	Appliance	kWh consumed
Water heater	500	Washing machine	120
Freezer	100	Stove	100
Lighting	100	Dryer	80
Dishwasher	35	Microwave oven	25
Electric iron	15	Personal computer	12
TV	10	Radio	8
Toaster	4	Clock	2

A simplified diagram of the cathode-ray tube; for Example 1.8.

A homeowner consumes 700 kWh in January. Determine the electricity Example 1.9 bill for the month using the following residential rate schedule:

Base monthly charge of $12.00.

First 100 kWh per month at 16 cents/kWh.

Next 200 kWh per month at 10 cents/kWh.

Over 300 kWh per month at 6 cents/kWh.

Solution:

We calculate the electricity bill as follows.

Base monthly charge = $12.00 First 100 kWh @ $0.16/k Wh = $16.00 Next 200 kWh @ $0.10/k Wh = $20.00 Remaining 400 kWh @ $0.06/k Wh = $24.00 Total charge = $72.00 Average cost = ______________ $72 100 + 200 +^{400 =} 10.2 cents/kWh

Referring to the residential rate schedule in Example 1.9, calculate the average cost per kWh if only 350 kWh are consumed in July when the family is on vacation most of the time.

Practice Problem 1.9

Answer: 14.571 cents/kWh.