# ATAT 105 Basic Electricity > # [[T105 Week 11| ◀️ ]]  [[T105 Home| Home ]]  [[T105 Week 13| ▶️ ]]               [[QR T105 Week 12| 🌐 ]] ># [[T105 Week 12|Week 12]] >- [[T105 Week 12#Impedance|Impedance]] >- [[T105 Week 12#Resonance in an AC Circuit|Resonance in an AC Circuit]] ># [[T105 Week 12#Lab|Lab]] >- [[T105 Week 12#MP 105-2 Practice|🔵MP 105-2 Practice]] >[!jbplus|c-blue]- Lesson Intro >### What >In this lesson you will learn about impedance and resonance. The effects on AC circuits of frequency is expanded to show the complete picture of opposition to current, as well as what the point of least impedance is. > >### Why > >More in your ever increasing knowledge about AC power in terms of aviation systems. Alternating current is more complicated than direct current, and so your knowledge must expand as AC is used extensively in aviation. > >## Approach and Objectives > >By understanding the following topics, you will have achieved the learning outcome for this lesson. Consult your course outline for the learning outcomes and other details of this course. > >### Course Learning Objectives > >CLO 10. Assemble a functional electrical circuit using components according to a given circuit diagram. >CLO 11. Show using a Digital Multimeter (DMM) the measurement of voltage, current and resistance in a circuit. >CLO 15. Identify factors that affect capacitive reactance and inductive reactance in an AC circuit. >CLO 16. Calculate total capacitance in series and parallel capacitive circuits. >CLO 17. Calculate total inductance in series and parallel inductive circuits. >CLO 18. Calculate the total impedance of an AC circuit. > >### Testing > >You will be tested on this material on Assignment 4 and the final test. Details [[T105 Intro#Testing and Grades|here]]. >[!jbplus|c-blue]- Prof >### Objectives > >In this lesson, impedance, which should be a comfortable combination of what we've learned last week and throughout the course. Resonance is also explained, preparing students for more on this later in the program. > > ### Theory >For the theory course, the formulas sum up the relationships. This is critical for the last MP. >### Lab >For the lab, practice for MP 105-2. This will be an important preparation for next week. ## Impedance ![[Pasted image 20210808214511.png|350]] You now know that the flow of current in an AC circuit is opposed by resistance (R), capacitance (C), and inductance (L). A circuit containing all three of these is often referred to as an RCL or RLC circuit. On the other hand, circuits containing only two of the three oppositions are referred to as resistive capacitive (RC) and resistive inductive (RL) circuits. ![[Pasted image 20210808214528.png|350]] Earlier in the course you learned that, through Ohm's law, the current in a circuit is equal to the voltage divided by the resistance. However, in an AC circuit you must also consider the effects of both capacitive and inductive reactance. The combined effect of resistance, capacitive reactance, and inductive reactance is called impedance and is represented by the letter Z. Like resistance, the unit of measure for impedance is the ohm. ![[Pasted image 20210808214604.png|350]] ![[Pasted image 20210808214648.png|350]] At first it may appear that you can just add the sum of the individual oppositions. However, this is not true since inductive reactance and capacitive reactance have opposite effects on a circuit. This difference is caused by the leading of voltage and current respectively. Remember ELI the ICE man. Because of this, you must determine the net effect of the two reactances. Consider: Inductive reactance X_L as positive because it causes the voltage to lead the current. And capacitive reactance XC as negative because it causes the current to lead the voltage. You can add the two quantities using the formula: Total Reactance = XL + (-Xc) ![[Pasted image 20210808214710.png|350]] Since inductive and capacitive reactance cause 90 degree phase shifts, they cannot be algebraically added to resistance to calculate impedance. However, they can be considered as two forces acting at right angles to each other. This is best illustrated through vectors. A vector is a quantity that has both magnitude and direction and is usually represented as an arrow. The length of the arrow reflects the strength or size of the quantity, and the direction of the arrow represents the direction of the quantity. A circuit's resistance is plotted on a horizontal line. Since reactance acts 90 degrees to resistance, it is plotted on a vertical line extending up from the tip of the resistance line. ![[Pasted image 20210808214749.png|350]] Using vector addition, you can now combine resistance and reactance into a resultant force which represents impedance. Using the pythagorean theorem, A2 + B2 = C2, you can determine the length of the resultant or impedance vector. This is illustrated in the formula: ![[Pasted image 20210808214852.png|350]] Simplified, the formula for impedance in a series circuit reads: ![[Pasted image 20210808214905.png|350]] ![[Pasted image 20210808214913.png|350]] It should be noted that this formula can only be used for a series circuit. With this in mind, consider a 400-hertz, 115 volt AC circuit with a total resistance of 100 ohms, inductance of 20 millihenrys, and capacitance of 5 microfarads. To begin, you must find the inductive and capacitive reactance. ![[Pasted image 20210808214947.png|350]] Since the capacitive reactance is larger than the inductive reactance, the circuit is said to be capacitive and the amps lead the volts. Now that you know the values for resistance, inductive reactance, and capacitive reactance, you can calculate impedance using the formula: ![[Pasted image 20210808215039.png|350]] Once impedance is found, you can use Ohm's law to determine circuit current. However, since the symbol "Z" is used to represent total opposition in an AC circuit, it takes the place of "R" in Ohm's law. Also note that the voltage used in Ohm's law in this case is V_RMS or V_AC since we are talking about AC voltage. ![[Pasted image 20210808215116.png|350]] The total circuit current is 1.10 amps. ## Resonance in an AC Circuit > [!aside]- Ref >[[Resonance|🗺️]] ![[Pasted image 20210808215159.png|350]] Let's review some of what we know about reactance, both inductive and capacitive. Inductive reactance in a coil is zero when the frequency is zero. However, as the frequency increases, the inductive reactance increases. Therefore, the higher the frequency, the more back voltage or counter EMF the inductor generates, and less current flows. This continues until the back voltage equals the source voltage, and no current flows. The reactance in a capacitor varies in the opposite way. For example, at a frequency of zero, no current flows through a capacitor, and therefore reactance is infinite. But, as the frequency increases, the capacitive reactance decreases until there is no capacitive reactance. Both of these relationships can be plotted on a graph. The lines representing the two reactances cross at the resonant frequency. In other words, a circuit's resonant frequency is that frequency where inductive and capacitive reactance are the same. The resonant frequency is expressed in units called Hertz, as you could have guessed. ![[Pasted image 20210808215315.png|350]] ### Resonant Circuits ![[Pasted image 20210808215426.png|350]] ![[Pasted image 20210808215433.png|350]] There are many different types of resonant circuits. In a series RLC circuit at its resonant frequency, the current flowing in the inductor and the capacitor are equal. However, they are 180 degrees out of phase with each other. The inductive and capacitive reactances are also exactly the same, but because of the phase difference they cancel each other, leaving a total reactance of zero. In this case, the total opposition offered to the flow of AC is that of the resistance. A circuit's impedance is minimum when at its resonant frequency and is equal to the circuit resistance. ### Parallel RLC circuits The following goes into parallel circuits, but we will not be covering this. It is included for your interest. In a parallel RLC circuit at its resonant frequency, a large amount of current flows between the capacitor and the inductor. This allows energy to first be stored in the electrostatic field of the capacitor and then in the electromagnetic field around the inductor. At the resonant frequency, the circulating current in the inductor and capacitor is high. There is almost no current supplied from the source though, so the source sees the parallel circuit as having a high impedance. The reactances cancel each other, and so the opposition is purely resistive. The power factor of the circuit is one. ## Lab In order to be prepared for MP 105-2, this week we will practice an exercise very similar to the MP. Now is the chance to make sure that all the concepts, and all your skills with the lab equipment are up to scratch. ## MP 105-2 Practice The last MP for this course is a culmination of several pieces of knowledge you have collected along the way. The circuit itself is familiar to you, as you have already performed measurements on it in previous labs, but for the MP, you will also be asked to calculate impedance. You can save time in the lab by downloading the [[MP105 2.pdf|MP worksheet]] and doing the calculations before the lab. As always, it is important that you understand the purpose of the lab activities. This MP allows you to demonstrate your knowledge of several key electrical principles, as well as your ability to use a multimeter for several different types of measurement, as well as a signal generator and oscilloscope for generating and measuring AC waveforms.