The resistor $R$ in Figure P 18.58 dissipates 20 W of power. Determine the value of $R.$
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Current, Resistance, and Electromotive Force
December 5, 2020
Hi, can I know how you got 81.66? thanks
in this particular problem, we are going to make use off series off equations to get the value of register are which is actually in the figure here. And we need to assume certain currents which are flowing through the thing So it start. But say step, eh? During this case, let forward to see Brady in register are be br which is Oh, 20 words I was given in bigger No let island I do and I three be the currents Thio file toward doom and for deal respectively. No, a blind case here that you already know that if you consider this particular terminal as, say a then some of the enduring currents is equal to some of the living colors that is gay troops, current law. So, Aunt No A If we consider Ivan is enduring and I do and I three of living information, Ivan is equal to ay two plus three. And let us consider this as equation. What? We're going to mark each and every question Now, Now let's apply just a baby. A plane, give you, do you play? That is a left concerted Luke which consists of components such a 75 world Fireman Turkey Abs. So applying gave you that escaped just for the low We are going to look ways and considering the living polarity across every company So started 75 75 minus five games Irony minus 30 times I do is equal to zero Therefore finally that we get Fi Ivan Lester G. I do is equal to 75 by changing the signs over. Let it be as immigration too. No Asper equation One We can say that I do is equal to ay one minus off i three We need to put this around you in equation too. So therefore what we get why I won Bless 30 times in Sure if I do, we are going to make Shin now I went minus I tree is equal to 75. So finally that we get 35 Byron minus 30 times between is equal do 75 again and mark this digression And this will be our equation. No, let's go to Step two and its market as step See on the stoop. No, we need to apply. Gave you to look too. So therefore we make sure he does minus 40 Plus our because 40 in our home resistances are in CDs. My deep worry about our three my tree bless 30 times I do is equal to zero. Yeah, that's market as equation for now Asper equation one again. But you already know that I do is equal to Ireland minus I three. We need to put this value in equation for therefore what would get here as minus four. Keep Lazar times I three, just 30 times. I won mine inside tree music with a zero solving this further We get 30 times, Ireland minus off. We're taking the terms off I three together now. So 40 yes are less 30 times I three is equal to zero. Therefore Turkey Time's Ivan minus off 70 plus our times I three is equal to zero starring further we get therefore turkey Ivan is equal. Do 70 plus our times I three So finally that we get Ivan is equal to 70. Bless our upon turkey. Put it in the bracket Times three. Now this is the main value off Ivan in themselves are an i t. We have already got it. Now that small boy put this when you in immigration me to calculate the value off by three. So therefore, what we get as 35 times Ivan minus 30 time I three Easy, Quick do 75. This is a question three that we already know. So therefore, 35 times let's put the value of firing that so indeed bless our upon 30 times I three minus 30 times I three is equal to 75. It's cool to the next page. Now resolve this further. Therefore, it's combined the dumpster just 35 70 and 30. Okay, so that combination will give me the value s it U N 0.663 less 1.167 are times I three minus 30 times. I three is equal to 75. Therefore, for the 51.66 times I three bless 1.167 Our names I three is equal to 75. Now that's mark this as gration number five. Okay, further moving it now. Louis, Right. Aggression off bobble with respect to huh? So therefore now you know that PR is expert too. Guidant. The whole square multiplied by its resistance. The current which is flowing through it is I three. So therefore taking Wantem off by three in the denominator of PR is equal to ay three times there. Therefore, now I three times are is equal to 20 watts upon Hi three. It's marked this as equation six because we're going to use it now. We may write it here. No, look, this value off I three times are immigration five because down on the left inside right now. So therefore, let's try this. So from a given 0.663 plus 1.167 times drink tea born I three, which is equal to 75 therefore 51.66 i three square bless 1.167 times drink tea. Do y did buy I three. He's equal to 75 you know. It's started out so 51.66 I three square minus off 75 times. I see when we dig that 75 come on the left hand side and plus it is going to be 23.34 is equal to zero is now This is the main requestion that we have got. No, that's more Now solving this further. That's considered the quadratic a question first. So for ratting aggression as we already know that eight times I three square less be times by three plus C is equal to zero. Now, when we compare the situation with respect to the previous one, I write the values for your reference. That is a secret of 51.66 bees equal to minus 75 and C is equal to 23.24 Therefore, to calculate the value of fighting, we will use this formula. We need to remember that minors be plus minus under your golf B squared minus for a C upon do, eh? This is what we're going to make use off to get the value off by three. So therefore, let's start creating, I think, is equal to since B is minus 75 so it becomes plus less minus. Andrew doll 75 square minus full time. 71.66 Might deployed by 23 point to you fool a born two multiplied by 51.66 Now careful value off trees IQ will do last 75 plus minus. Trained G eight form +32 will do the calculation very carefully. Here. 103.32 That is the multiplication that your court. So this is the way. Once we need to plus on, once we need to minus. So what we're going to get is we'll just separate the dorms together For your reference they do. Upon 103.32 or 75 minus 28.3. Dube upon 103.32 which is equal to one beer are a 0.451 hate and beer. Now these are the two Wellies off. I think that we already got. It's more headed with this. No, we need to make use off question six. So here, using immigration. Six. Okay, forward to get value off. You are. This is our aim. So therefore I three times are is equal to cranky upon night. It is a question six, which we already know so therefore are is equal to trendy of born I three square. So let's make use of one venue first. That is strained Dearborn One square which is equal to train de homes. Similarly using the same aggression I'm accusing I t s 0.451 in tempura. So let's calculate that Ali is equal to so this equation that means same I'd be square so cranky upon. Let's make use off other value of Phi 30.45 on it square. So we get the value off. I are as 97.98 which is equal to we can take it as 90 domes. Now these are true values. Ah is trendy on our as 98 homes. So we just write down the finance it here with us. Anyone off though values offer a distance are can be used. That is either drink Humes or nine gauge rooms and this is gonna be our find an answer.