Capacitor calculations - Basic calculations for capacitors in series and parallel

capacitors are used in many circuits for different purposes so we're going to learn some basic capacitor calculations for dc circuits in this video capacitors typically look something like this we have an electrolytic and a ceramic type capacitor the electrolytic is polarized meaning one side must be connected to the positive and the other side must be connected to the negative the ceramic type can generally be connected either way on the side of the electrolytic capacitor we find a dashed line which indicates the negative side one lead is also longer than the other which indicates the positive side however these are normally trimmed down during installation so you shouldn't rely on this alone these two capacitors are represented with symbols like these notice the polarized capacitor has a small plus symbol indicating the positive side when connecting to a dc supply the voltage of the battery will push electrons into the capacitor and so the capacitor charges up to the same voltage as the battery capacitors are charged nearly instantly when connected directly to a battery but we nearly always use a resistor this will delay the charging time and later on in this video we'll see how to calculate that inside the capacitor lots of electrons have built up on one side they are prevented from moving across due to the insulating material between the two sides as electrons are negatively charged we therefore have a build up of charge on one side compared to the other therefore we have a voltage difference between the two leads these electrons are held in place and the capacitor can hold this charge for very long periods of time when given a path they will discharge until the capacitor is empty electrons do not pass through the capacitor they simply build up inside and are then released the amount of charge stored in a capacitor is calculated using the formula charge equals capacitance in farads multiplied by the voltage so for this 12 volt 100 microfarad capacitor we convert the micro farads to farads then multiply this by 12 volts to see it stores a charge of 0.0012 coulombs if we needed to store a charge then we just divide this by the voltage in this case 12 volts to see we need 17 microfarads we can calculate the energy stored in a capacitor using the formula 0.5 multiplied by the capacity in farads multiplied by the voltage squared so if this 100 microfarad capacitor was charged to 12 volts we convert the micro farads to farads and then drop these numbers into the formula to see it is storing 0.0072 joules of energy we know that the capacitor will charge up to the voltage of the battery so if we connect a capacitor like this what will the voltage across the capacitor be it will be 1.5 volts if we connected a capacitor like this what will the voltage be it will also be 1.5 volts these are just two different ways to connect capacitors in our circuits we have series and parallel the configuration will cause the capacitors to perform differently if we place a capacitor in parallel with a lamp when the battery is removed the capacitor will begin to power the lamp it slowly dims as the capacitor discharges if we use two capacitors we can power the lamp for longer let's say capacitor 1 is 10 microfarads and capacitor 2 is 220 microfarads how do we calculate the total capacitance well that's very simple the answer is 230 microfarads the capacitors combine in parallel so 10 plus 220 equals 230 microfarads we can keep adding more such as a 100 microfarad capacitor and the total is just the sum of all of the capacitors by placing them in parallel we are essentially combining these to form a larger capacitor that's very useful because if for example we needed a large 2000 microfarad capacitor but we didn't have one we could just use more smaller capacitors such as 2 1000 microfarads or 4 500 microfarads etc it's also often used for filtering out noise and to provide more current in high demand circuits the total charge stored in parallel circuits is just charge equals the total capacitance multiplied by the voltage so here we have a 9 volt battery and two capacitors with a total capacitance of 230 microfarads as this is parallel this wire is 9 volts and this wire is 0 volts so both capacitors are charged to 9 volts therefore 23 micro farads multiplied by 9 volts will give us 0.00207 coulombs and with the three capacitors we have 330 microfarads we multiply this by the nine volts to get 0.00297 coulombs we can also calculate the charge of each capacitor individually we just use the same formula for each capacitor you can see the answers on screen for that now if we place a capacitor in series with a lamp when we press the switch it will illuminate but then becomes dimmer as the capacitor reaches the voltage level of the battery once it achieves this the lamp will be off remember electrons do not flow through a capacitor because of the insulating material inside the electrons are simply accumulating inside on one of the plates and as they accumulate they are rejecting an equal amount of electrons off of the opposite plate so a current can only flow when the capacitor charges or discharges currently with the battery removed there is no way for the capacitor to discharge so it will hold the voltage at the same level it doesn't matter if we connect or disconnect the battery the lamp will not turn on however if we provide another path when the switch is pressed the capacitor can now discharge so the electrons can flow through the lamp and illuminate it this will become dimmer as the capacitor discharges what if we had two capacitors connected in series again capacitor 1 is 10 microfarads and capacitor 2 is 220 microfarads how do we find the total capacitance for that we use this formula it might look difficult but it's actually very simple all we need to do is input our capacitor values of 10 and 220 microfarads we can type it like this on our calculator or into excel which gives a total of 9.56 microfarads notice that the total capacitance is now smaller than the lowest value capacitor if we added a third capacitor of 100 microfarads to the circuit we get a total capacitance of 8.73 microfarads so it has decreased even more that's because by combining these in series we're essentially increasing the thickness of the insulating material so the attraction of the negatively charged electrons to the positively charged holes on the opposite side will become weaker the total charge of the series capacitors is found using the formula charge equals capacitance in farads multiplied by the voltage so if we use a 9 volt battery we convert the micro farad to farads and see the total charge equals 0.008604 coulombs the total charge for the 3 series capacitor circuit is therefore 0.00007857 coulombs the charge held by each capacitor individually is very easy to calculate in the series circuits that's because it's the same as the total charge each capacitor holds the same number of electrons when in series and that's because when we charge the capacitors the current was exactly the same in all parts of the circuit the same number of electrons that were pushed into one plate were pushed out of the opposite plate so each series capacitor can only ever be charged to the same level the smallest capacitor will therefore be the limiting factor however because each capacitor can hold a different capacity the voltage of each capacitor will be different we find the voltage of each capacitor using the formula voltage equals charge in coulombs divided by the capacity in farads so for this circuit we see that capacitor 1 is 7.8 volts capacitor 2 is 0.35 volts and capacitor 3 is 0.78 volts these combine to the total voltage of the battery which is 9 volts let's say we have a 9 volt battery a 100 microfarad capacitor a 10 kilo ohm resistor and a switch which are all in series the capacitor is fully discharged and we read zero volts across the two leads when we close the switch the capacitor will charge the voltage will increase until it is the same level as the battery the voltage increase is not instant it will have an exponential curve at first the voltage increases rapidly and then it slows down until it reaches the same voltage level as the battery we split this curve into six segments but we're only interested in the first five because at the fifth marker we're basically at full voltage so we can ignore anything past this each segment represents something called a time constant therefore as we have five segments we have five time constants so it will take five time constants to charge the capacitor from zero to just under one hundred percent all we need to do is to calculate how long one time constant is and then we multiply this by five to calculate the time constant we use this formula time constant in seconds equals the resistance in ohms multiplied by the capacity in ferrets so we convert our resistor to ohms and our capacitor value to farads and we see that 10 000 ohms multiplied by 0.0001 farads equals one so in this example the time constant is equal to one second therefore five of these is five seconds meaning it takes five seconds for the capacitor to fully charge to 9 volts if the resistor was just 1000 ohms the time constant would be 0.1 seconds so it would take 0.5 seconds to reach 9 volts if the capacitor was 1000 microfarads it would take 50 seconds in total coming back to our original circuit we can therefore calculate the voltage level at each time constant at point 1 the voltage is always 63.2 percent 0.2 is 86.5 0.3 is 95 0.4 is 98.2 percent and 0.5 is 99.3 percent so the voltage will never actually reach 100 that's also why we stop at just five points so in this example after one second the capacitor voltage is 5.68 volts after two seconds it's 7.78 volts after three seconds it's 8.55 volts after four seconds it's 8.83 volts and after 5 seconds it's 8.94 volts if you needed a more precise answer we could also calculate each point like this remember because this is in series the current of the circuit decreases while the voltage of the capacitor increases once at full voltage no current will flow in the circuit if the resistor was a lamp it would therefore instantly reach full brightness when the switch was closed but then becomes dimmer as the capacitor reaches full voltage when we provide a path for the capacitor to discharge the electrons will leave the capacitor and the voltage of the capacitor reduces it doesn't discharge instantly but follows an exponential curve we split this curve into six segments but again we're only interested in the first five at point one the voltage is always thirty six point eight percent point two will be thirteen point five percent point three will be five percent point four will be 1.8 percent and 0.5 will be 0.7 percent for example if we had a 9-volt battery a lamp with a resistance of 500 ohms and a 2 000 microfarad capacitor our time constant would be 500 ohms multiplied by 0.002 farads which is one second so at the very moment the battery is disconnected the capacitor will be at 9 volts and as is powering the circuit the lamp will also experience 9 volts after one time constant in this case 1 second the voltage will be 36.8 percent which is 3.312 volts at 2 seconds it's 1.215 volts at 3 seconds it's 0.45 volts at 4 seconds it's 0.162 volts and at 5 seconds it's 0.063 volts so the lamp will be illuminated for just under 3 seconds obviously this will become dimmer towards the end of the three seconds okay check out one of the videos on screen now to continue learning electronics engineering as this is the end of this video don't forget to follow us on facebook twitter instagram linkedin and of course the engineeringmindset.com

Channel: The Engineering Mindset

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Keywords: capacitors, capacitance, capacitors in series and parallel, electrical engineering, capacitor, capacitors in series, step by step science, series circuits, voltage, farad, circuits, capacitor in series and parallel, capacitors explained, capacitors in parallel, parallel plate capacitor, dielectric, energy stored in capacitor, electronics engineering, energy stored in a capacitor, voltage source, circuit theory, electrolytic, capacitors and resistors, series circuit, bigclivedotcom, dc

Id: ucEiEic-kZ4

Length: 16min 16sec (976 seconds)

Published: Sun Apr 04 2021