# Audel electrical course for apprentices and journeymen - Rosenberg P.

ISBN: 0-764-54200-1

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The law that bears his name is Ohmâ€™s law. This law gives the relationship between voltage, current, and resistance in an electrical circuit. This law is accurate and absolute. When we come to alternating current, we will find that it still applies, with a few other factors being involved.

Statement of Ohmâ€™s Law

The fundamental statement of Ohmâ€™s law is as follows:

The current in amperes in any electrical circuit is numerically equal to the electromotive force (emf or voltage) in volts impressed upon that circuit, divided by the entire resistance of the circuit in ohms. The equation may be expressed

where

I = intensity of current in amperes E = emf in volts R = resistance in ohms If any two quantities of this equation are known, the third quantity may be found by transposing, as

E = IR R = E/I and I = E/R

Analogy of Ohmâ€™s Law

Hydraulic analogies may be used to illustrate electrical currents and the effect of friction (resistance). We all know from experience

71

72 Chapter 5

that water running through a hose encounters resistance. Thus with X pounds of pressure at the hydrant, we will get a considerable flow of water directly out of the open hydrant. If we use 50 ft of 3/4-in hose, the flow will be cut down, and if we use 100 ft of 3/4in hose, the flow will be cut even more. The same will be true if we use 50-ft-long V2-in hose: We get less water with the same X pounds of pressure at the hydrant than we did with the 3/t-in hose. The X pounds of pressure may be compared to volts. The quantity of water delivered may be compared to current (amperes), and the friction (resistance) of the various hoses may be compared to the resistance of the conductor in ohms.

Illustrations of Ohmâ€™s Law

Now, if we deliver 100 volts to the circuit in Figure 5-1A and the load resistance is 50 ohms, there will be a current of 2 amperes:

T E 100V

= R = 500 =

In Figure 5-1B, we have the same voltage but the load resistance is 100 ohms, so we find

I = R = 100V = A R 100 O

Then, in Figure 5-1C, we have doubled the voltage to 200 volts and have 50 ohms of load resistance, so

T E 200V

I = â€” =---------= 4 A

R 50 O

Here we see that doubling the voltage on the same load as in Figure 5-1A will double the current from 2 to 4 amperes.

Problem 1

An incandescent lamp is connected on a 110-volt system. The resistance (R) of the heated filament is 275 ohms. What amount of current will the lamp draw? Answer:

I = R = HO = â€œ-A

Ohm's Law 73

(A) With 50-0 resistance.

(B) With 100-0 resistance.

(C) With 200-V emf and 50-0 load.

Figure 5-1 Examples of Ohm's law.

Problem 2

We have two electric heaters with resistances of 20 and 40 ohms, respectively. We also have 120 and 240 volts available. Calculate current amperes for the following combinations:

â€” 120 V

a. 20 ohms on 120 volts: I = â€” = = 6 A

K 20 12

r 1 o a t/

b. 40 ohms on 120 volts: I = â€” = An ^ = 3 A

K 40 n

â€” 240 V

c. 20 ohms on 240 volts: I = â€” = = 12 A

K 20 n

â€” 240 V

d. 40 ohms on 240 volts: I = ~ = .â€ž ^ = 6 A

K 40 n

From the above problems, you may readily see that doubling the resistance on the same voltage halves the current; also, doubling the voltage with the same resistance doubles the current.

From this the deduction may be made that the current in any circuit will vary directly with the emf and also that the current in an electrical circuit varies inversely with the resistance. Also, if the current in an electrical circuit is to be maintained constantly, the resistance must be varied directly with the emf; on the other hand, if the emf is to be kept constant, the resistance must be varied inversely with the current.

74 Chapter 5

Ohmâ€™s Law and Power

There is another series of equations related to Ohmâ€™s law because of the fact that the power in watts in any electrical circuit is equal to the current in amperes multiplied by the emf in volts. Thus:

P = EI where

P = power in watts I = current in amperes E = emf in volts

This formula may be transposed to find either I or E. Thus:

PP I = â€” and E = â€” EI

So if P = 100 watts and I = 4 amperes, we find E = P/I, or 100 W/4 A = 25 V. Since R = E/I and E = P/I,

R = P/I2, I2 = P/R and I = VWR, and P = I2R

Then, if P = 100 watts and R = 4 ohms, then I2 = 100 W/4 O = 25 A2, and the square root of 25 is 5, so I = 5 amperes. Further, since P = EI and I = E/R, we have:

E2/R = P R = E2/P E2 = RP and E = 2rP

If R = 4 ohms and P = 100 watts, then E2 = PR = 100 W X 4 O = 400 V2. The square root of 400 V2 is 20 V. Thus, E = 20 volts.

The Ohmâ€™s Law Circle

One of the easiest ways to remember, learn, and use Ohmâ€™s Law is with the circle diagram shown in Figure 5-2. This Ohmâ€™s law circle can be used to obtain all three of these formulas easily. The method is this: Place your finger over the value that you want to find (E for voltage, I for current, or R for resistance), and then the other two will make up the formula. For example, if you place your finger over the E in the circle, the remainder of the circle will show I X R. If you then multiply the current times the resistance, you will get the value for voltage in the circuit. If you wanted to find the value for current, you would put your finger over the I in the circle, and then the remainder of the circle will show E ^ R. So, to find current we divide voltage by resistance. Lastly, if you place your finger over

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