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Question 4Rz ANMR3Determine the equivalent resistance of the circuit: Express~ whole your answer to the nearest number and do not include units in your answer Ri-lo...

Question

Question 4Rz ANMR3Determine the equivalent resistance of the circuit: Express~ whole your answer to the nearest number and do not include units in your answer Ri-lohms, Rz-Sohms, R3-3ohmsand the battery voltage 9v

Question 4 Rz ANM R3 Determine the equivalent resistance of the circuit: Express~ whole your answer to the nearest number and do not include units in your answer Ri-lohms, Rz-Sohms, R3-3ohmsand the battery voltage 9v



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In Fig. $27=14$, take $R_{1}=$ $10 \Omega, R_{2}=15 \Omega$, and $R_{3}=20 \Omega$. If the potential difference across the ideal battery is $\Delta V_{\mathrm{B}}=15 \mathrm{~V}$, find: $($ a) the equivalent resistance of the circuit, (b) the current through each of the resistors, and (c) the total current in the circuit.

So in this question we have the following circuit so we've got the battery attached to a resistor. What do you like that? Yeah in other resistor like that. So first let's figure out or let's make a chart of our information. So voltage current resistance. Okay and we need column rose for 123 for in our total. Okay And the label are resistors 1 2 or and three. So what we know is that we're just for one is 100 arms resistor two is 50 homes, Resistor three is 50 owns register four is 75 homes. So first let's figure out where our series parts of our circuits are and where are parallel starts. Parts of our circuits are so we've got one loop that can go this way, you've got one loop that can go that way And we've got one loop that can go that way. So what we have is resistor one is in series with everything But then resistors 2, 3 and four are in parallel with each other. Mhm. So first let's figure out our resistant, we're trying to figure out the equivalent resistance of our circuit. Okay so first we got to figure out the equivalent resistance of just are parallel section and what we can do that is one over are too was one over R three Plus one over R four Equals one over our total. So we got one over 50 homes plus 1/50 homes plus one over. Yeah. Yeah 75 homes equals one over R. T. So what I would suggest doing is get a decimal answer on the left side and then do one divided by that decimal. So for this section we get the our total to be 18.75 homes. Okay now this is in parallel with the other section So are I mean it's in serious the other section so R1 plus this 18.75 homes. Well give us the overall equivalent resistance of our circuit so 100 Plus or 18.75 and run into sig Figs. This is going to give me a total resistance of 1 18.8 owns. So that's our answer to part A. Yeah. Now it's going to some of the other information that we have, we know that the battery has a voltage or an EMF of 6V which also means that there is for you anything else, what we can do is across this bottom row, across my total row we can figure out our total total current using I equals V over R Which be 6V divided by R118 8 Holmes Which gives me .0505 imps Yeah. Okay so now part B von so what is the current and resistance want? Well since resistor one is in series with everything, the current is the same as the total, all of the current has to go through that resistor. Mhm What this allows us to do next Is figure out the voltage at resistor one again using arms law the equals ir That's a .5 yeah. Oh five times more 100 homes Because it's a voltage at your sister. one Of 5.5V. Okay. The next boxes we can fill in is the voltage in 23 and four. And the way we can do this is we know that the voltage in resistor one has to add With the voltage and resistors 2 3 and four which is going to be the same. He is the parallel circuit. More parallel section. So 2 3 and four are often seen all of the same voltage. And that boulder tends to add up with 5.5 to get the six. So this is .95V. You need box and then last not least to go across each of our rose again. We're gonna use Homes law of I equals the over our. And those are answers for C. The and E. Yeah. And the way that we know that we are correct. The way that we can check ourselves if Is those three red numbers should add up 2.0505. And they do. So our total resistance is 1 18.8 owns Our current and resistor 1.0505 Amps. And then two and three are 30.190 amps. And resist their 4.127 amps

The door boulder This gents across the circuit is rt, which is a short distance I want nos are too arty, divided by our hopeless rt 28 plus four p x 20 Divided by 30 plus drink we get for the home the total current then i d. It was to eat by rt, which is the coastal 10 by 40 deedle want to five on beer So rt total distances or be home and total current I think it was Dedo blanche, bullfight and beer.

Portion we're just talking about power and current in circuits and this is a two part problem. So first from answer questions A and the uh just kind of qualitatively. And then we'll answer them again quantitatively when they give us um some hard numbers and then we'll chat goes with art. Um are qualitative answers from apartment or from the first part of the question. So in uh initially they ask us for a qualitative analysis of power in august circuits. Ask us to rank the power from uh from greatest to least in each of these circuits to call A. B. C. And D. Okay, so you'll notice that uh also could have the same configuration but um either have one or two are uh for the resistors and either one or two B from their voltages. All right, so let's start with the definition for power. So P is equal to I squared R. But we're not given are initially they're excusing i initially or just given BNR but we know how to relate this through variable season jones paul says that the C. I. R. So thus is equal to be over arm. So you can substitute that into this equation. So we'll have P. Is equal to B squared over R. Times. Are the squared over R squared times are? So this is equal T. V squared overall. Alright so now for each circuit we just have to plug in uh either one or T. V. And either one or two are and I'll give us our different powers. So uh when we do this we find that the greatest power is see and then followed by D. Uh huh. Than be. So this is just our qualitative ranking of the current in all the different expectations. And in part B they ask us for the current in each of these circuits. Right? So here we're just gonna use on small remember is equal to be over arm. So we can just plug in either one or two B for B. And either wanting to our for our So when we do this, the currents that we where and we rank them. I find that I see is the greatest, followed by A. Which is the same as I'd. And then finally I be with the smallest current. Alright, So now they're going to give us some numbers to plug in and then we'll check our results of this. All right. So they tell us that the voltage of the battery.

So we are given that resistors are two artery and awful are connected in parallel, which means that the key violent resistance can be found by the reciprocal matter, which means that one over equivalent resistance will be given by some off the reciprocal lt's off on the three day existence that they're connected in battle. In must simplifying this equation, we will get our Vicky Valent to be equal to our to our three are four overs not to Artie less are two are four this artery artful and substituting the values because the equivalent resistance to the 18.8 rooms. Now again, this parallel combination is in cities that it is a stir odd one. And this means that the totally gay violent resistance. So let me just like this to the RP, which means that this is the equivalent assistance off the parallel combination. On the total equivalent, resistance will be some off our one on dhe rp with these two are connected in cities and this become sequel toe 118 point Edel's. So this is the equivalent resistance for the whole night. Look now for part B, we have to find the current flowing to odd one. So the current flowing through all one can be found by simply dividing the M F bye. This is resistance. Odd one on this with the equal door, 5.75 times. Thank God, the five minus two. And so I'm not right aching explicitly all the values and solving them because I'm basically using the same notation as given in the problem. So it's pretty easy for you to know what are the values because in the problem also are Renato artery there the same notations and I'm just using the corresponding values to substitute. So yeah, mister, I'm saving some time by not writing the values again. So now we need to find the current flowing through. But the sister Arto, Arto Artie and awful are in parallel combination. So to find the current flowing through any off these three resistance, we first need to find the voltage. Ah, the voltage difference across So any of these three distress sisters because they have the same world. It's difference. I said, Don't do that. Let's find radio. It is the oldest difference across my sister are too. So that is equal to so basically that can be given by subjecting the e m f by the void is difference across our one. It is given by whom slow on this is needed because Oops. Okay, so let me just connick this one. So I buy mystically road are one. So this is actually our equivalent. Okay, so now coming toe the world It's difference a lot across the resistant arto. So since I want our one on our toe in fact, out to our tree on our fourth. So these three are in battle and this whole thing is connected in cities with argon, which means that the voters difference across our one on the waters difference across Oh, any of these three Oh, resistors must add up to give the totally in f and therefore in order defying the boldest difference off the parallel combination. They're subtracting the bold. It's difference across our one from the totally a mess. I hope that makes sense. So now that we have this began find I do my own slaw, which is dividing the corresponding voltage by the corresponding resistance on this will give the value off current Toby 1.9 times 10 to the party minus two AM Pia. So that's the current flowing through a sister. I do. It is the start. Our tour. So now then we have to find the current. Yeah. So this is the current flowing through resistor arto. Then we have to define We have to find the current through our tree. So again we can find this. By whom? Snow which is Vetri? Always our tree. Now instead, off going through all the calculations one more time, we can instead simply use this value again over here because Vito Vetri before one must be equal to each other because our tree are four and Otto are in parallel and we know that no, the voters difference across pattern really connected as the stores is same. So this will basically be goingto rito over our tree And again we can substitute this expression over here on DDE. Find that the current comes out to be 1.9 times 10 to the five minus to an appeal. Now, instead, off again doing this calculation on there's one another shortcut knicker, uh, by which you won't need Thio go through this step as well. On that is, if you see our tow. An artery are same. The voter equal toe 50 owns on dhe. They have the same boulders difference as well. So naturally, the current flowing through what the resistor should be equal. So I three must in fact the equal Do I do on dhe, that's all. You can get the answer. Oh, just by, uh, noticing that thing instead off doing this calculation again. Okay, so now coming to the third part the last one way, we have to find the current flowing through resistor are for so for that, we can use junction drawing. So according to junction, will we have the current? I distributed two i three i for I do I try and I for because the tree, this reader, is this tree Ah, are the current's flowing through the resisters that connected in battle. So the colin gets divided when entering that parallel combination. So from here, you can find i four to be equal toe Ivan minus I to minus I tree. And then we can substitute these three values from the previous parts over here and get the courage to be 1.25 I understand the burden minus two rabbia. Thank you.


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