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Circuit Elements - Sources and Best Problem Solving Method

Like what we discussed in the previous section about how important is an element as a basic building block. Literally, an electric circuit is an interconnection of the elements. How we determine the voltage, current, and even power of specific elements in electric circuits is called circuits analysis.
circuit element

Make sure to read what is dc circuit first.

Circuit Elements

There are two types of elements we will find in electric circuits: passive elements and active elements. The difference between these two is the active element is able to generate energy while the passive element is unable to do so. Examples of passive elements are resistors, capacitors, and inductors. Examples of active elements are generators, batteries, and operational amplifiers.

The most important active elements are voltage and current sources which able to deliver power to the connected circuit. These two sources can be divided again into 2 groups: independent and dependent sources.
Ideal independent source is an active element which produces a specified voltage or current that fully independent of other circuit elements.
For a more scientific definition, an ideal independent voltage source delivers to the circuit whatever how much required current to maintain the terminal voltage. The examples of this ideal independent voltage sources are batteries and generators. 

Figure.1 shows the symbol of independent voltage sources. Those two can represent dc voltage sources but only Fig.1(a) can represent time-varying voltage source.
independent voltage source symbol
Figure 1. Independent voltage source symbols

For the same explanation, an ideal independent current source is an active element which produces specified current completely independent of the voltage across the source. Independent current source will deliver current to the circuit whatever voltage in the circuit. The symbol itself is presented in Figure.2 where the arrow indicates the flow direction of current i.
independent current source symbol
Figure 2. Independent current source symbol

The second type of source is the ideal dependent (or controlled) source.
An ideal dependent (or controlled) source is an active element which the source quantity is controlled by another voltage or current.
The symbol itself is presented by diamond-shaped symbols in Figure.3 where Fig.3(a) is a dependent voltage source and Fig.3(b) is a dependent current source. There are four possible types of dependent sources depend on the voltage or current controlling the source :
dependent source symbol
Figure 3. Dependent source symbol
  1. voltage-controlled voltage source (VCVS)
  2. current-controlled voltage source (CCVS)
  3. voltage-controlled current source (VCCS)
  4. current-controlled current source (CCCS)
Dependent sources are very useful for modelling purpose of transistors, operational amplifiers, or integrated circuits. The example of a current-controlled voltage source is shown in Figure.4 at the right side where the voltage 10i depends on current i through element C.
Current controlled voltage source example
Figure 4. Current controlled voltage source

Must be noted that voltage source (dependent or independent) will deliver any required current to maintain the terminal voltage is as stated. For the same idea, the current source will provide the required voltage to ensure the stated current flow.

Make sure to read the definition of the current source and what is voltage source to completely understand the explanation above.


Circuit Elements Examples

To understand the explanation better, let us review the examples below :
1.Determine the absorbed power or supplied power for each element in Figure.5
current controlled current source example
Figure 5. Example of the current-controlled current source

Solution:

For p1, the 5A current is out the positive terminal, then
 p1 = 20 (-5) = -100 W → Supplied Power
For p2 and p3, the current flows into the positive terminal, then
 p2 = 12 (5) = 60 W → Absorbed Power
 p3 = 8 (6) = 48 W → Absorbed Power
For p4, take note the voltage is 8 V with positive terminal at top same as voltage of p3. Since the current flows out of the positive terminal, then
 p4 = 8 (-0.2I) = 8 (-0.2 x 5) = -8 W → Supplied Power
We should observe that -20 V independent voltage source and 0.2I dependent current source are supplying power to the rest of the network, while the other 2 absorbing power, then
 p1 + p2 + p3 + p4 = -100 + 60 + 48 - 8 = 0

Applications

This section will cover two practical applications of basic electric circuit concepts. The first one in the TV picture tube and the second is how to calculate electricity bills.

TV Picture Tube

The application of the motion of electrons can be found in both the transmission and reception of TV signals. TV camera reduces a scene from an optical image to an electrical signal at the end of transmission end. The scanning process will occur with a thin beam of electrons in an iconoscope camera tube.

At the receiving end, the image is constructed using a cathode ray tube (CRT) located in the receiver. The CTR is represented in Figure.6 When iconoscope tube produces an electron beam with constant intensity, CRT beam varies in intensity depending on the incoming signal.

Cathode ray tube component
Figure 6. Cathode ray tube

The electron gun at high potential fires electron beam. The beam passes through two pairs of plate both vertical and horizontal deflections so the spot on the screen where the beam strikes can move right, left, up, and down. After the beam hit the fluorescent screen, it gives light to that spot and a picture is shown on the TV screen.



Electricity Bills

The second application to deal with is electricity usage which charged by the electric utility company to us, customers. The cost depends on how much energy we consumed in kilowatt-hours (kWh). However, if a customer does not use energy at all, there is still a minimum payment charge to the customer to pay as connecting electricity service. The interesting thing is, as the energy consumption rises, the cost per kWh will drop. Let us see the Example below :
2. A family consumes 700 kWh in February. Calculate its electricity bill with a residential rate schedule below :
  • Base monthly charge : $12.00
  • First 100 kWh per month : 16 cents/kWh
  • Next 200 kWh per month : 10 cents/kWh
  • Over 300 kWh per month : 6 cents/kWh
Solution :
$12.00 = Base monthly charge
$16.00 = First 100 kWh @$0.16/kWh
$20.00 = Second 200 kWh @$0.10/kWh
$24.00 = Remaining 400 kWh @$0.06/kWh
$72.00 = Total charge

Average cost = $72 / 600 = 10.2 cents/kWh


Problem Solving

The basic principle of problem-solving will remain the same whatever the different complexity and magnitude.
The steps will be :

  1. Define the problem carefully.
  2. Present everything you know about the problem.
  3. Establish a set of alternative solution and decide one which has the greatest chance of success.
  4. Attempt a problem solution.
  5. Evaluate the solution along with the accuracy.
  6. If the solution is satisfactory, present the solution; if not, repeat from step 3.
Read the explanation below :
1. Define the problem carefully. This first step is the most important part of the process because it becomes the foundation for all the steps. In a simple explanation, you need to understand the problem completely. Make your time to identify the problem with some help from any individual related-field.
2. Present everything you know about the problem. Write down every possible methods or solution you know.
3. Establish a set of alternative solution and decide one which has the greatest chance of success. Every problem will have a number of the path to find the solution, so it is wise to find any alternative possible help to save your time and stress, including software packages which may help you greatly along with high accuracy.
4. Attempt a problem solution. This is the time to begin solving the problem. Any attempts must be well documented in order to find a successful solution or to revise the unsuccessful. The detailed revision may be the best solution for the problem and even simpler alternative solution.
5. Evaluate the solution along with the accuracy. Evaluate deeply about the solution, is it worth to present to your boss, team, or whoever it is?
6. If the solution is satisfactory, present the solution; if not, repeat from step 3. Proceed with the presentation of the solution or revise it once more if it leads to other problems or alternatives.
Have you understood what is the circuit elements? Don't forget to share and subscribe! Happy learning!
Reference:  Fundamentals of electric circuits by Charles K. Alexander and Matthew N. O. Sadiku

Untuk Bahasa Indonesia baca Elemen Rangkaian - Sumber Tegangan dan Arus
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