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Q1. Three capacitors each of capacitance 9 pF are connected in series.(a) What is the total capacitance of the combination?(b) What is the potential difference acro...

Question

Q1. Three capacitors each of capacitance 9 pF are connected in series.(a) What is the total capacitance of the combination?(b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply?

Q1. Three capacitors each of capacitance 9 pF are connected in series. (a) What is the total capacitance of the combination? (b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply?



Answers

Three capacitors each of capacitance $9 \mathrm{pF}$ are connected in series. (a) What is the total capacitance of the combination? (b) What is the potential difference across each capacitor if the combination is connected to a $120 \mathrm{~V}$ supply?

So this question belongs to the capacitance in which we have three capacitors which are connected in parallel. So this is the circuit diagram for this question. Okay. Uh these are three capacitors and this capacitor is of to pick a fairer and this is of three. Pick a fairer and this is of four. Pick a fairer. Okay. And this combination are connected in parallel. So for the part we have to calculate the total capacitance of the combination. So see for this parallel combination it is seven plus C two plus C. Three and substituting the value. So seven is to pick a fairer plus C two is three, pick a fairer and C three is four. Pick a fairer. So from here we get a Cuban and capacitance of the system is nine people feral. Okay, so this becomes the answer for the part of the problem. Okay now for the part B we have to determine the charts on each capacitor. If connect if the capacitor combination is connected to the 100 world power supply. Now if 100 world is connected to this capacitor system then each capacitor will get a potential of 100 world because all are in the parallel. So we can calculate the charge Q. Which is given by CV. So charge on the to pick a fairer to pick off error. It will be equals to pick off error, manipulated by potential which is 100 gold. So from here we get charge is equal to 200 people figured. Sorry PICO column. Or it can be written as to manipulate and to the power minus 10 Fulham and similarly charged on the three PICO fairer capacitor. This will be three PICO fairer manipulated by 100 world. Okay so from here we will get charge. E. Is equal to 300 PICO column. Or it can be written as three molecular weight. And to the power minus stan ulam and similarly charged on the four pic of a red. It will be four PICO fairer molecular by 100 volts. So from here we get 400 PICO column and it can be also written as four molecular bait and to the power managed and cool. Um, so these are the values for the charge on the each capacitors. Okay.

In this question we have two capacitors in series. Yes, you won in c. two and then it is connected Across the power supply. 120 votes. Yeah. And then see one is given to be uh one of them micro fire it C two is when 500 Micro Harry. He's So we want to find There are four parts in this question. You want to find a total capacitance? Yeah. So this is capacitors in series. It will be using one over kill. He goes to one of us the one last one of us to so if you uh I can calculate C equivalent immediately by all right, during this. Okay, take some of the reciprocal and then after that you take the reciprocal and that. So in two days you get uh six times 10 to the negative four mary. Okay, so this is the I should say 6 6.0. Yeah. He said this is the answer for part A and then maybe you want to find a charge on each capacitor. Okay so because they are in serious the charge on each process is the same. Uh huh. It's the same day. 21 because fuck you too goes to see equivalent times we so 6.0 times 10 to the negative fall Multiply by 120 Again 3.072 columns. Mhm. So this is the answer for a bee and then you can't see you want to find a potential difference across each capacitor. So we're using QE goes to C. V. So we can complain. Everyone goes to Q one over C. One key one is your point there were seven to C one S 1000 Micro Ferret. Hey so you get 72 votes And then we too will just be (399 31 320 1972 you get 48 votes. So this is the answer. These are the answers for Patsy and then Pandey. Uh we want to find a total energy start by their capacities. Okay so you can complete you want to go soon. Uh here we go. So have cd square. Okay, so the total energy start Okay. Is half ce que square. Yeah, Half times six times and to the 94 times 120 square. Okay, so when you do this, okay, This is what you get 4.32 juice. So this is the answer by this question and that's all.

16.40. So we have two capacitors, and we're told that in parallel they have an equivalent capacitance of nine pico Harrods. And in Syria's they have an equivalent capacitance of to Pico parents. And so we want to find the values of the two capacitors. So in parallel, capacitance is ad, so just be C one plus C two is equal. The nine Pico Jared's or C one is going to be nine Pico Fair. It's minus C two. This will allow us to eliminate, see one in a minute here and then capacitors in Siri's at the same way that resistors and parallel do so. The reciprocal sze of the capacitance add up to be one over to Adam to be the reciprocal of the equivalent capacitance. No, this is to Pico parrots. Um And then, like I said, put again our expression for C one to eliminate it. I'm C one is nine pico fare ads minus C two, but then we get a plus C two. So there's no sea too. And the denominator now so, uh, rearranging this, we're going to get C two squared minus nine Pico Jared's C two plus 18. He Co Farid Squared equal zero. So we have a quadratic equation or, um, for C two. So you can either use the quadratic formula or noticed that you can factor this. So we have seen to minus six Pico Jared's time. See too minus three pico Harrods people. Zero. So now see to is either going to be six pico ferrets or three pico Jared's and then see one is going to be nine Pico Fair. It's minus C two, but notice that if C two is three Pico Jared's, then see one will be six and vice versa. Here, um, so it doesn't really matter which is which just that one of them has to be three Pico Baird's and the other one has to be six Pico Jared's.


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