# ATAT 105 Basic Electricity > # [[T105 Week 10| ◀️ ]]  [[T105 Home| Home ]]  [[T105 Week 12| ▶️ ]]               [[QR T105 Week 11| 🌐 ]] ># [[T105 Week 11|Week 11]] >- [[T105 Week 11#Inductive Reactance|Inductive Reactance]] >- [[T105 Week 11#Capacitive Reactance|Capacitive Reactance]] ># [[T105 Week 11#Lab|Lab]] >- [[T105 Week 11#AC and Induction|AC and Induction]] >- [[T105 Week 11#AC and Capacitance|AC and Capacitance]] >[!jbplus|c-blue]- Lesson Intro >### What >In this lesson you will learn about inductive and capacitive reactance. This opposition to current flow happens only in AC circuits, and we will see that the frequency of the AC affects the reactance. > >### Why > >Another few steps 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. > > >### 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, reactance, both inductive and capacitive. We have to rely on students having kept up until now, and we can help to connect or build on previous knowledge. > > ### Theory >For the theory course, the formulas sum up the relationships. Once the idea of phase shift is solid, it comes down to calculating it. This is critical for the last MP. >### Lab >For the lab, the measurements confirm the relationship between frequency and the two types of reactance. For some students, once they have seen it, they need to go back to the theory to make sure that it makes sense to them. ## Inductive Reactance ### Back EMF Review what you know about [[T105 Week 8#Inductance|inductance]]. Inductance includes the the behavior of a coil of wire in resisting any change of current through the coil. This resistance is from the counter electromotive force or counter EMF or back EMF, and is based on Lenz's law. So when we apply a DC current to an inductance, after a short period of time the current will stabilize and the counter EMF disappears as no lines of flux are crossing the conductor. However, when the conductor carries an AC current the direction and amount of current flow continually change. So a continually opposing induced voltage acts on the current and is called inductive reactance. Inductive reactance appears like a resistance, but only applies to AC currents. You could (but shouldn't) refer to it as AC resistance, but it is reactance. It is measured in Ohms like resistance. ### Reactance and Frequency ![[Pasted image 20210808201225.png|350]] As inductance increases, inductive reactance increases. This should make sense to you if you look at counter EMF like the back force when blowing up a balloon. The more air you try to force in (current) the more the balloon want to blow the air back out (reactance). As it turns out, the higher the frequency, the quicker the lines of flux are crossed, with a resultant increase in back EMF. So, as frequency increases, inductive reactance increases. ### Inductive Reactance Formula Inductive reactance is represented by the symbol $X_L$ and is measured in ohms. The formula for determining inductive reactance is: $ X_L=2 π f L$ Where: $X_L$ = Inductive Reactance $π$ = 3.14159 $f$ = frequency in Hertz $L$ = inductance in Henrys Apply what you know about the [[T110T SSGW05#Formula Relationships|relationships in a formula]] such as this. >Inductive reactance is proportional to the inductance within a circuit and the frequency of the alternating current. Let's look at an interesting way to apply what you already know to explain why this applies only to AC circuits. Simple multiplication also tells you that if the frequency is zero, as it is in direct current, there is no inductive reactance. This makes sense since there is no changing magnetic field in direct current. However, as the frequency increases above zero, the amount of change in the magnetic field increases. This, in turn, causes the inductive reactance to increase. ### Power Loss Remember that the opposition produced by induction is caused by the generation of a counter, or back, electromotive force. But, unlike the opposition caused by resistance, no heat is generated in a circuit with inductance, and, therefore, no power is dissipated. ### Phase relationships ![[Pasted image 20210808201605.png|350]] If a circuit is purely inductive, that is, there is no resistance present, current does not begin to flow until the voltage rises to its peak value. Then, as the voltage begins to drop off, the current rises until the voltage passes through zero. On a sine wave, this condition is represented by a 90 degree shift in phase. ![[Pasted image 20210808201622.png|350]] In other words, in a purely inductive circuit, the change in current lags the change in voltage by 90 degrees. With a 90 degree phase angle the power factor is zero and there can be no [[true power]]. This is because the negative power produced cancels the positive power. In other words, the load returns as much power as it receives. ![[Pasted image 20210808201759.png|350]] If an inductor of the proper size is placed in series with a light bulb, the inductive reactance causes most of the source voltage to be dropped across the inductor. In this case, the bulb burns very dimly, if at all. ![[Pasted image 20210808201834.png|350]] ![[Pasted image 20210808201840.png|350]] ### 400 Hz Alternating Current Most aircraft use 400-hertz alternating current. This is because the inductive reactance at this frequency is high enough to allow smaller transformers and motors to be used. In other words, the frequency part of the formula is raised, and thus we don't have to build a larger inductor, with more coils etc, to achieve the reactance we want in the circuit. This then results in significant savings to the weight of the aircraft, and you know [[T101 Week 2#Weight|why that is important]] in aviation. The difference in the specifications required for the different frequencies is something that you must respect as a technician, of course. But you can understand that if an inductor designed for 400-hertz AC is used in a 60-hertz circuit, the lower inductive reactance caused by the lower frequency might allow enough current flow to burn out the transformer. Conversely, if a 60-hertz transformer is used in a 400-hertz circuit, there is so much inductive reactance that the efficiency of the transformer becomes too low for practical use. ## Capacitive Reactance ![[Pasted image 20210808201904.png|350]] Capacitive reactance is the opposition to the flow of alternating current caused by the capacitance in a circuit. The symbol for capacitive reactance is $X_C$ and it is also measured in Ohms. It is like inductive reactance in that it appears to be resistance, but only applies to AC circuits. ### Capacitive Reactance Formula Here we have another formula whose form is not completely alien to us: $ X_C = \frac {1}{2\pi fC}$ Where: $X_C$ = Capacitive Reactance $\pi$ = 3.14159 $f$ = frequency $C$ = capacitance Again, our math knowledge tells us that a circuit's capacitive reactance is inversely proportional to its capacitance and frequency. Be clear that this means that as the capacitance rises, the capacitive reactance decreases. This is also true for frequency: As the frequency increases, the capacitive reactance decreases. The reason for this is that as a circuit's capacitance increases, more current must flow to charge the capacitor. At the same time, if a circuit's frequency increases, a capacitor charges and discharges more often, resulting in more current flow. The greater the current flow, the less the capacitive reactance. ### Phase Relationships ![[Pasted image 20210808202039.png|350]] In a purely capacitive circuit, the current leads the voltage by 90°. We saw in a [[T105 Week 9#Capacitors in Circuits|capacitive circuit]] that the current must flow into the capacitor before the voltage across it can rise. If you slow down the process, your knowledge of electricity will explain the graphics here. When the capacitor is fully charged, the voltage is at maximum and the current is at zero. As the capacitor begins to discharge, the current begins to flow and the voltage starts to drop. ![[Pasted image 20210808202056.png|350]] The current flow is greatest as the voltage passes through zero. As the voltage begins to build in the opposite direction, the current flow starts to drop off until the capacitor is fully charged. ![[Pasted image 20210808202111.png|350]] Since the current leads the voltage by 90 degrees in a purely capacitive circuit, the power factor is zero and no real power is produced. This is because the negative power equals the positive power. The concepts of resistance and reactance are important for your understanding of the dynamics of an AC circuit. This video [[Y Resistance Reactance|🎞️]] has graphics that are animated, and unlike what was presented in this lesson. They may be a good way for you to imagine what is happening. It is highly recommended that you listen closely to what is said and ensure you are with the process at each step. The very last minute of this video deals with impedance which we will see next week. ## In the Lab This week we will demonstrate the relationship between frequency and reactance, both inductive and capacitive. You will build a simple circuit, inject a waveform at a specific frequency, and then measure current and voltage so we can observe the resultant reactance. You could fill out Column 1 of tables 2 and 4 before the lab, as they are calculations based on the component values. # Lab [[T105L WS11.pdf|Worksheet]] [[T105L SAFETY|Safety Briefing]] ## AC and Induction Build the following circuit: ![[Pasted image 20211115045544.png|350]] Use the wire pieces of the training aid to resemble the following: ![[Pasted image 20211115045634.png|350]] ### Waveform Generator On the waveform generator, Select channel and set the output load to Hi Z. Then, set up a sine wave with a frequency of 800 Hz and an amplitude of 10 V_pp. ### Ammeter For current measurements, set the multimeter to ACI, connect the red lead to 100ma and black lead to common, and replace wire piece "A" with the meter leads. Polarity, that is, the negative and positive leads (black and red) do not matter with AC measurements, as the polarity switches constantly. ### Voltmeter For voltage measurements, ensure leads are correctly inserted, select ACV, and use autorange. Measure voltage across the inductor, that is, one lead on either side of the inductor itself. Record your measurements in Table 1 on your lab worksheet. Continue by entering the frequency from the table in the waveform generator. Do not readjust the voltage or output settings. > Be certain that you have your multimeter correctly set up, including ensuring current measurements are in series. ### Calculations For each frequency in Table 2, fill in the first column using this formula: $X_L = 2\pi fL$ For each frequency in Table 2, fill in the second column using your measured values and this formula: $X_L = \frac {V}{I}$ The differences between the two can be attributed to the following reasons: - the internal impedance of the signal generator and the resistance of the inductor are added to the measured value. - inductors have a specified range where the relationship between frequency and reactance is linear. Outside of this range, the difference between calculated and measured values will be greater. ## AC and Capacitance Build the following circuit: ![[Pasted image 20211122183034.png|350]] Use the wire pieces of the training aid to resemble the following: ![[Pasted image 20211122183149.png|350]] ### Waveform Generator On the waveform generator, Select channel and set the output load to Hi Z. Then, set up a sine wave with a frequency of 50 Hz and an amplitude of 10 V_pp. ### Ammeter For current measurements, set the multimeter to ACI, connect the red lead to 100ma and black lead to common, and replace wire piece "A" with the meter leads. Polarity, that is, the negative and positive leads (black and red) do not matter with AC measurements, as the polarity switches constantly. ### Voltmeter For voltage measurements, ensure leads are correctly inserted, select ACV, and use autorange. Measure voltage across the capacitor, that is, one lead on either side of the capacitor itself. Record your measurements in Table 3 on your lab worksheet. Continue by entering the frequency from the table in the waveform generator. Do not readjust the voltage or output settings. > Be certain that you have your multimeter correctly set up, including ensuring current measurements are in series. ### Calculations For each frequency in Table 4, fill in the first column using this formula: $X_C = \frac {1}{2\pi f C}$ For each frequency in Table 4, fill in the second column using your measured values and this formula: $X_C = \frac {V}{I}$ The differences between the two can be attributed to the minor difference in values of the capacitor.