Electrical Sources theory and study

Voltage Source

Current Source

Dependent Sources

potential difference

driving force.

Figure 01-01

R_i

R_L

A-B

i_L

R_i

A-B

V_RL

(E.M.F.)

R_i

R_L

V_RL

V_AB

V_AB = V_RL = V - R_i i_L

A-B

the A-B

positive pole

negative pole

(D.D.P.)

R_L

R_L = ∞

R_i

DDP

EMF

10 megaohms

2. Types of Sources

2.1.Independent Sources

2.1.1.Voltage Sources

Voltage sources are sources that ideally provide constant tension in their output terminals, regardless of the load. In practice, however, its output voltage is a function of the load, that is, the higher the load, the lower the output voltage. This is due to its internal resistance, as has already been explained in Item 1 (Introduction). As examples, we can cite common batteries, alkaline and rechargeable, commonly used in flashlights, portable radios, MP3, MP4, etc...

"unloaded"

EMF

If it is ordinary batteries, we must get rid of them, because there is no way to recover them. However, if it is batteries or rechargeable batteries, there is a way to recover them by simply using a "charger". This appliance makes it circulate current by the internal part of the cell battery or battery, in the opposite direction, causing a reduction in the internal resistance and with this we say, after a certain time of recharge, that the battery is charged. This will allow them to be used normally, as if they were new. In general, we can repeat this process from 500 to 1000 times, depending on the type of battery or batteries and its manufacturer.

In addition to cell batteries or batteries, today we have as sources of voltage electro/electronic appliances, from the simplest like the cell phone chargers, to other very complex and specific types.

2.1.2. Sources of Current

1000 ohms

12 V

1000 ohms

10 ohms

1.2 mA

10 ohms

In the Figura 01-02 we see an example of the current source and the symbol used to represent it in a basic circuit. Notice that the current I will circulate by the resistance R and on this we'll have a voltage drop equal to V_R = R I.

2.2. Dependents Sources

Figure 01-03

I₂

g₁₂

V₁

g₂₁

3. Sources Association

Figure 01-04

Figura 01-05

V₁ > V₂

I₁ > I₂

4. Explosion Sources Techniques

"source explosion"

Figure 01-06

2-ohm

8 ohms

2 A

Figure 01-07

8 ohms

2 A

"ground"

e₁

2 A

e₂

e₃

4 ohms

3 ohms

Figure 01-08

e₁

e₂

With this we obtain a single source of current which value is 1 A, leaving the node e₂ and coming to the node e₁. The Figure 01-09 show the new transformation of the circuit.

Problem solving: click here!

5. Millman's Theorem

Millman's Theorem allows us to reduce any number of voltage sources in parallel into a single source. See as an example the circuit shown in Figure 01-10.

This transformation will allow us to calculate the electric current that flows through the charge R_L or the voltage between its terminals without applying methods such as Kirchhoff, law of Knots, Norton's theorem and others. Therefore, we must understand how to apply this theorem. Let's summarize it in three steps.

Step 1

We must convert all voltage sources into current sources using the source transformation (access Source Transformation Method clicking here! ). See what the resulting circuit looks like in Figure 01-11.

Step 2

After executing the source transformation, we must add the values of the current sources that resulted from the transformation. Carefully observe the polarity of the sources and the calculation of the resulting equivalent resistance. See what the resulting circuit looks like in Figure 01-12.

Step 3

After the two steps above were performed, an equivalent current source was created in parallel with the equivalent resistance of the circuit. Now, we apply the source transformation again to obtain an equivalent voltage source in series with the equivalent resistance. Okay, we have the transformed circuit. See the result in Figure 01-13.

Now, simply by applying Ohm's law to the circuit it is possible to calculate the electric current in the charge R_L, as well as the potential difference across it , V_ab .

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