# Course 7: Electronics

Electronics Topic 4: Capacitors All copyright and intellectual property rights in respect of materials developed by the service provider during this project will vest in the Department of Higher Education and Training, which will have the right to allow any individual, company, agency or organisation to use or modify the materials for any purpose approved by this Department, including selling the materials or releasing them as Open Educational Resources (OER) under an appropriate copyright license. Assumed prior learning 05_01_00 05_01_02 05_02_01 05_03_01

05_04_01 Outcomes By the end of this unit the learner will be able to: Explain the terms Impedance and Capacitive Reactance in AC circuits and use their symbols correctly. Describe how Capacitive Reactance changes with capacitance and frequency. Calculate the total capacitance of capacitors in series and parallel. Unit 4.3: Capacitors in AC circuits

Introduction In the previous unit, we had a look at the characteristics of a capacitor in a DC circuit. But what happens when we put a capacitor into an AC circuit where the voltage and current are constantly changing? Before, we start answering this question, we should make sure we understand what

alternating current is. Alternating Current Alternating current alternates. Instead of current always flowing in the same direction, AC changes direction back and forth all the time like the water in the animation. Click the button to watch a short explanation of the difference

between DC and AC. Difference between DC and AC The AC sine wave We saw in that last video that we use the shorthand of AC to describe current AND voltage that alternates. We also saw that we most often show AC as a nice smooth

wave the sine wave. Click the button to learn more about AC and this sine wave. Alternating Current Average AC Because voltage and current in AC are always changing, we cannot just use the peaks as an indication of power of the supply. We need something else.

Watch the video to see how we can calculate a useful average voltage or current of an AC supply. Vid01 RMS examples 1. A 6V AC supply will have a peak voltage of 6V/0.707 = 8.49V. 2. A 230V mains supply has a

peak voltage of 230V/0.707 = 325V. 3. AC with a peak current of 12A will have an RMS current of 12A x 0.707 = 8.48A. = . = . When dealing with AC,

Always assume that values given are RMS UNLESS otherwise indicated. Quick quiz question 1 If an AC peak voltage is 380V, what is the RMS voltage? a) b) c) d) 269V

537V 380V 266V Quick quiz question 2 If an AC RMS current is given as 6.25A, what is the peak current? a) b) c) d)

3.13A 4.42A 6.25A 8.84A Quick quiz question 3 If an AC current is given as 12A, what is the RMS current? a) b) c) d)

16.97A 8.48A 12A No way to tell AC power Take a few minutes to get more familiar with AC by playing with our AC simulator. Download and work through the worksheet. Then watch the video to make sure you completed everything correctly.

Download the worksheet Vid02 Build the Circuit To continue our exploration of capacitor characteristics, recreate this circuit from the previous unit. Build this circuit. Rollover or touch each symbol in the schematic to find out more. Watch the video if you need help.

Watch how to build the circuit and set up your multimeter Step 1 Open the stopwatch app on your mobile phone. Close the switch and time how long it takes for the current through the circuit to reach about 0.7mA or 700A A Time to reach 0.7mA Check

s Img05 Current falls Even if your time in step 1 was not about 10s, you should have noticed that the current in the circuit kept falling. Why do you think this happened? As the capacitor charged up a) The voltage of the battery decreased. b) It became harder for the negative plate of the capacitor

to accept more electrons as so fewer electrons could flow until no more electrons were able to flow. c) The capacitor voltage decreased. Discharge your capacitor To discharge your capacitor, simply connect an LED in series with a 470 resistor to the capacitor. Just make sure that you connect the LEDs anode to the side of the capacitor that was connected to the positive terminal of the battery.

Once the LED no longer shines for about 2-3 seconds, the capacitor is discharged Img06 Step 2 Redo the experiment as before, but this time see what happens to the current after about 60s. Current after 60s

Img07 mA Check Step 3 Calculate the time constant for this capacitor. Remember T = RC. Img08

RxC= Check Step 4 Based on the voltage and the resistance of the resistor, what is the maximum current that can flow in the circuit? What is 37% of this value? mA Max current

37% of max current Check Img09 mA The time constant for current You should be able to see where all this is going. The time constant tells us when a capacitor has charged to 63% of the applied voltage. It also tells us when the current will be

down to 37% of its maximum value. Watch the video to find out more. Vid04 What we know so far So far, we have seen that in a DC circuit, when a capacitor is fully charged, no current flows through the circuit. It is like the capacitor has infinite resistance.

Vid05 But what happens in an AC circuit when the voltage is always Watch the video to see changing as is the direction of the how capacitors behave in AC circuits. current? Capacitors in AC circuits You probably dont have access to an AC power supply, so we need to keep investigating with virtual circuits. Download and work through the

worksheet. Then watch the video to make sure you completed everything correctly. Download the worksheet Vid06 Capacitive Reactance Click each number to see what we have learnt. We call the resistance offered by capacitors in AC circuits 1 Capacitive Reactance (Xc).

2 Capacitive Reactance (Xc) decreases as the frequency of the AC power increases. Capacitive Reactance (Xc) decreases as the capacitance of 3 the capacitor increases. 4 The total resistance to current in an AC circuit is called Impedance (Z). Z = R + X

A Virtual Circuit Lets use a simulation to see the potential real life effects of capacitive reactance. Download and work through the worksheet. Then watch the video to make sure you completed everything correctly. Download the worksheet Vid07

Capacitators in Series and Parallel We now know that capacitors offer resistance to the flow of current in an AC circuit in much the same way as resistors do. We call this kind of resistance capacitive reactance. Do capacitors in series and parallel behave the same as resistors in series and parallel? Lets find out. Img14

Capacitors in Series and Parallel We are going to explore capacitors in series and parallel with a virtual circuit. Download and work through the worksheet. Then watch the video to make sure you completed everything correctly. Download the worksheet Vid08 Capacitators behave opposite to

resistors We have just discovered that when capacitors are in series, their total capacitance decreases and that when capacitors are in parallel, there total capacitance increases. They behave in the opposite way to resistors. Img16 Capacitators in Parallel

It turns out that capacitors in parallel work the same way as resistors in series. Capacitors in PARALLEL Resistors in SERIES Img17 Img18 Capacitators in Series It turns out that capacitors in series work the same way as

resistors in parallel. Capacitors in SERIES Resistors in PARALLEL Img19 Img20 Test Yourself We have come to the end of this unit. Answer the following questions to make sure you understand how capacitors

behave in AC circuit. Video Briefing Vid01 (1 of 3) Create a screencast vide presented by an expert electrician explaining RMS voltage/current in AC systems. Base explanation on https://www.allaboutcircuits.com/textbook/alternating-current/chpt-1/measurements-ac-magnitude/ . Use similar images to those on page 3. 1. AC is always changing value. What value do we give it? Can we use peak values even though, most of the time the AC is less than the peak value? DC is easy because voltage and current are always the same. 2. We could try the average but, for any sine wave this is zero (A). 3. We could make all the negative values positive(B) first and get an average this way.

4. But this average is not the same as the supplys ability to do work or its power. It is slightly less. Remember that P = V2/R or I2R. There are squares involved. 5. Having a measure that allows us to compare the power delivered by different AC supplies and between AC and DC supplies would be useful (C). Video Briefing Vid01 (2 of 3) 1. This 10V AC is called the Root Mean Square or RMS value. You dont need to know the maths behind this. You just need to know that RMS = Peak of the AC x 0.707. 2. RMS of an AC voltage or current is the equivalent DC voltage or current that would deliver the same amount of power. RMS is sometimes called DC equivalent. 3. The conversion factor of 0.707 ONLY applies to AC sources that are sinusoidal. Other waves forms have different conversion factors.

4. For sine waves the average voltage or current = Peak of the AC x 0.637. 5. Because RMS allows us to make better comparisons it is almost always used instead of Average. 6. When dealing with AC always assume that the values given are RMS values UNLESS you are told otherwise. Video Briefing Vid01 (3 of 3) Document Briefing Doc01 Create an annotated PDF worksheet with the following steps. 1. Make sure you have downloaded the EveryCircuit App from your app store. 2. If you are working on a computer, visit http://everycircuit.com/app/. 3. Open the EveryCircuit app and signup. After your trial, you will still have access to EveryCircuit and

other peoples circuits. You will just not be able to create your own circuits. 4. Go to the community space and search for the circuit called NOC_AC. 5. Open the circuit. 6. The circuit is being powered by a 220V AC power supply running at 50Hz. This is the same as your plug points at home. The animation speed is set to 20ms/s which means that each cycle takes 1 second to complete. The wave next to the power supply, shows the voltage. The graph above the circuit shows the current and the dots on the circuit show the movement of the electrons. 7. What is the maximum current through the circuit? What is the Root Mean Square or RMS current through the circuit? What is the RMS voltage of the circuit? Video Briefing Vid02 Create a video presented by an expert presenter working through Doc01 and answering the questions

with the aid of http://everycircuit.com/circuit/4691379468107776. Show that 1. That current is a max when voltage is a max. Show by adding voltage to the graph. 2. The light bulb is brightest when current is a max. 3. Changing the voltage has no effect on frequency but does affect current (Ohms Law) 4. Changing frequency has no effect on voltage or current 5. Show how to calculate RMS from peak: RMS = peak x 0.707. Video Briefing Vid03 Create a video presented by an expert presenter showing step-by-step how to build the circuit on a breadboard. The presenter needs to explain the following: 1. Add the capacitor, resistor, ammeter and the switch in series to the breadboard make sure of the capacitor polarity

2. Connect them to the power rail 3. Set up the multimeter to measure the current in the appropriate range 4. Connect power rail to battery Video Briefing Vid04 Create a video presented by an expert presenter explaining the following with the aid of a similar graphic. Also use the virtual circuit at http://everycircuit.com/circuit/5290262825009152 to help explain. 1. T = RC tells when a capacitor will get to 63% of the voltage applied to it.

2. T = RC also tells us when the current in the circuit will get to 37% of its maximum value. 3. The same is true (theoretically at least) for 5T. 4. We could see that as the capacitor charged, the current flowing through the circuit decreased. It decreases in exactly the same way as the voltage across the capacitor Video Briefing Vid05 Create a video presented by an expert presenter showing, in principle, how a capacitor behaves in an AC circuit using https://www.youtube.com/watch?v=NInt1Ss3vQ4 as a guide. 1. In DC, current only ever flows in one direction. We know that as a capacitor charges up, current flow decreases until the capacitor is at the same potential as the power source and no more

current flows. Capacitor acts as a break something with infinite resistance. 2. In AC, the voltage and current increase and decrease and change direction (show the sine wave and explain positive as voltage and current in one direction and negative as V and I in opposite direction). 3. Lets call the cap plates 1 and 2. 4. We turn the power on and the capacitor starts charging until voltage is a max. Electrons flow through the wires onto plate 1 and off plate 2. 5. As voltage reaches a max and starts to drop, the PD across the cap is greater than the power Document Briefing Doc02 Create an annotated PDF worksheet with the following steps. 1. Make sure you have downloaded the EveryCircuit App from your app store.

2. If you are working on a computer, visit http://everycircuit.com/app/. 3. Open the EveryCircuit app and signup. After your trial, you will still have access to EveryCircuit and other peoples circuits. You will just not be able to create your own circuits. 4. Go to the community space and search for the circuit called NOC_Capacitor in AC Circuits 1 5. Open the circuit. 6. At the moment, we have a 20V AC power source that is running at 1Hz. This means that the voltage completes one complete cycle once every second. The simulation is running in real time, so you can see that the wave next to the power source reaches the same point once every second. 7. We also have a 10VF capacitor in the circuit. There are no other resistors in the circuit so the only thing that could provide resistance to the flow of current is the capacitor 8. We can also see that, because the switch is open, there is no current flowing.

Video Briefing Vid06 Create a screen capture video presented by an expert presenter showing showing how to do all the calculations in doc01 using the simulation. 1. At the end explain that while the capacitor does offer resistance to current, it does so a bit differently from ordinary resistors in that its resistance is because of the AC current. So we give its resistance another name. We call it Reactance (X). We call the reactance of capacitors, capacitive reactance and the symbol Xc (X for reactance and c for capacitor). But we still measure reactance in . 2. Because we now have 2 types of resistance (normal resistor resistance and reactance) in an AC circuit, if we have both of these in a circuit, we need another new word for their total. We call this Impedance and give it the symbol Z. 3. Therefore, in a circuit with only normal resistors Impedance (Z) = Resistance (R)

4. In a circuit with only reactance Impedance (Z) = Reactance (X) 5. And in a circuit with both Impedance (Z) = Resistance (R) + Reactance (X) Document Briefing Doc03 Create an annotated PDF worksheet with the following steps. 1. Make sure you have downloaded the EveryCircuit App from your app store. 2. If you are working on a computer, visit http://everycircuit.com/app/. 3. Open the EveryCircuit app and signup. After your trial, you will still have access to EveryCircuit and other peoples circuits. You will just not be able to create your own circuits. 4. Go to the community space and search for the circuit called NOC_Capacitor in AC Circuits 2 5. Open the circuit. 6. You can see that we have 2 x 12V lamps, one of which is connected in series with a 10VF capacitor.

Everything is connected to a 12V AC supply running at 50Hz (the same frequency of the AC electricity that comes out of our plugs. 7. Flip the switch. Which lamp shines brighter the one connected to the capacitor or the other one? 8. What do you think will happen if we increased the capacitance of the capacitor? Would the lamp Video Briefing Vid07 Create a screen capture video presented by an expert presenter showing showing how to do all the calculations in doc01 using the simulation. 1. Explain that the lamp in series shines less brightly initially because it is in series with something that is providing resistance to the flow of current = less current = less light. 2. As we increase the capacitance, we decrease the capacitive reactance and so less resistance =

more current = more light. Document Briefing Doc04 (1 of 2) Create an annotated PDF worksheet with the following steps. 1. Make sure you have downloaded the EveryCircuit App from your app store. 2. If you are working on a computer, visit http://everycircuit.com/app/. 3. Open the EveryCircuit app and signup. After your trial, you will still have access to EveryCircuit and other peoples circuits. You will just not be able to create your own circuits. 4. Go to the community space and search for the circuit called NOC_Capacitors in Series and Parallel 5. Open the circuit. 6. There are 2 circuits. In the top circuit there are two 10VF capacitors in series and in series with

one of the light bulbs (L2), although one of the capacitors is currently shorted out of the circuit by S2 being closed. In the bottom circuit there are two 10VF capacitors in parallel. Both circuits have a 20V AC power source that is running at 50Hz. [Embed images of the 2 circuits with the switches and lamps labelled see next slide.] Document Briefing Doc04 (2 of 2) Video Briefing Vid08 Create a video presented by an expert presenter explaining how capacitors in series and parallel behave based on http://everycircuit.com/circuit/5031175566655488. Work through doc01 and its questions. 1. Opened S1. L1 shone more brightly than L2 as expected because L2 was connected in series

with a capacitor which offered resistance to the flow of current to L2. 2. If we open S2 to add the second capacitor in series we would expect L2 to shine more brightly. More capacitance means less reactance so more current to flow through L2. 3. But when we opened S2, L2 shone LESS brightly. Less current was allowed to flow = more reactance = less capacitance. So when we added a second capacitor is SERIES we got less capacitance like resistors in PARALLEL. 4. Opened S3. L3 shone more brightly than L4 as expected because L4 was connected in series with a capacitor which offered resistance to the flow of current to L2. 5. If we close S4 to to add the second capacitor in parallel we would expect L4 to shine less

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