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Write matrix equation that determines the loop currents.For each matrix _ let row correspond t0 loop row correspond to loop 2_ and Also enter positive values for po...

Question

Write matrix equation that determines the loop currents.For each matrix _ let row correspond t0 loop row correspond to loop 2_ and Also enter positive values for positive voltages and negative values for negative voltages_

Write matrix equation that determines the loop currents. For each matrix _ let row correspond t0 loop row correspond to loop 2_ and Also enter positive values for positive voltages and negative values for negative voltages_



Answers

Write a matrix equation that determines the loop currents. [M] If MATLAB or another matrix program is available, solve the system for the loop currents.

Okay, So in this proper and face on the cardinal formula, um, we know that the voltage you closed to the total current I turns on the total resistance in each group. So based on this equation, we can ride out for difference for different equations for each loop. So for the first look, we have six I one miners. I ju equals toe 30. Um, this for the second group, we have miners, I want plus nine times I to minors. For I three equals to 20. The third loop is minors. For I to a class seven I three miners two times I four equals to 40. And for the last hope, we have minus 203 plus seven. High four equals to 40. And we can turn worth this system of equations into the into a matrix form. I just collect this coefficient in front, off each variable I want try for and put them in a metrics. And then times are column vector. So I want I chew. I've read in 94 he closed to the wattage in each look. And, uh, once we once we write out this metrics, we can use the calculator. Teoh, get the solution to this system off equations, and I just direct you write it out. Okay, so this is the solution to this equation.

It is. So in this program we use the cooking off equation the water gee, close to the total current tons. Total resistance in each Duke clear. So, by this formula for the first rope, we have 12 I one miners, seven I to minors four times I forward close to 40. Well, a second look, minds seven i one plus 15 to minus six. I three equals the federal minus six I to plus 14 high three miners five by four because to 20 for the last loop, minus 41 plus 13 high for minors. Five i three cost minus to be careful about the last loop because you can see that's the direction off that battery. Um, it's different with the direction of the current. So, um, either we put a negative sign here or put a negative Saiful off this left inside part. So by this construction, we can ride out its magics from just collect off its Corey visions, and you can see that this convention metrics is actually symmetric and multiply this nature expired column vector because to the wattage we can use, um, we can use the software or calculator to solve this to self this system of equations by are using these metrics form. So we have I have the following result. I want, of course, believe in times 43. So this is the solution to this our system of equations.

Okay in this program where? Use the curtain off formula. What age? Because to the total current times your total resistance. Um, so we have five different lobes in a way that means we have five different immune equations. So for the first GOP at NYU, I want minus eyes. I tu minus. I fall minus four times I five because 2 50 the second group minus. I want cross seven. I tu minus twice off I three minus three. I five equals to 30 so he should be minus 30. So be careful about this. On the direction of the ah batteries, I eyes different with the direction of current. That means we have a miner's in front off this wattage for the third group minus two. I two pass tonight three minus three. High four minus three. I five equals to 20. The next group we'll be miners. I want minus three. I three process seven I four miners 25 because to minus 40. So there's another 90. If sign here for the same reason. And for the last hope, we don't have any pottage. That means the total body gee, close to zero, and we can convert this system of equations into matrix form by collecting off its coefficient. Yes, we have. No, I minus 10 minus 14 So I can see that this coefficient metrics is, in fact symmetric, not deprived by, um, the variables. I want to high five. You closed to the wattage, and we can use, um calculator to figure out on the solution. Justin, put this matrix into the calculator. We have I one equals 24 0.0 to a close to minus 4.38 Hi. Three close to minus 2.90 I fall. He caused to a minus 5.0. And I five equals two miners. Your point. Nice six. So this is a solution to this. It's not be prisons.

It is given that the system off unity questions to Ivan plus four i three is equal. Toby 10. I don't plus four. I three is equal Toby then and I one plus I to minus I three is equal. Toby zero now big competing Where Ivan I to and I to represent the talent and then the present. The wordage? No, by comparing it with the standard system. Off equations, we get the coefficient matrix. A is equal to be metrics with entries to 0401411 minus one. And the value X is equal to be three gross one metrics with entries. I even I too tight tree and B b A tree Gross. One metrics with entries 10 10 0 Now we need to find Dr Dominant trophy. Now that determinant off a is equal to be two multiplied with minus one minus four plus zero multiplied with zero minus four plus four multiplied zero minus one. Now we're simplifying. It will become minus 14 which is no tickled zero. So we can say that animals off the coefficient metrics a exists Now we know that it was is equal. Toby a joint off a divided by that determinant trophy. Now we're putting the lift, the tournament trophy. And by using the concept off co factors finding the value for doing OK, we get this will equal to minus one upon 14 while deployed with three close three metrics with entries minus 54 minus one four minus six minus. Do minus four minus age. Do No e X is equal to be so. From here we get the value of X is equal to be a university. Now we're putting the well of inverse and B we get to the value of X is equal to minus one upon 14. My deployed with three close three metrics with entries minus 54 minus one four minus six minus two minus four minus it two. And by putting the value of B which is equal Toby 10 10 0 Have a simplifying it. We get the value. Fax is comes out, Toby. 0.711 point for 22.14 So we get the value of couldn't even is equal. Toby Cedar, 0.71 ampere The value if I two is equal, Toby 1.42 ampere and the value of I tree is equal to be 2.14 ampere


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