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Problem 10.8-918 W3.2Hi(t)Vs(t)mF13 $2In this circuit the voltage source voltage is Va(t) 25 cos(10 t ) Vand the current source current is i(t) 5.0 A_The inductor c...

Question

Problem 10.8-918 W3.2Hi(t)Vs(t)mF13 $2In this circuit the voltage source voltage is Va(t) 25 cos(10 t ) Vand the current source current is i(t) 5.0 A_The inductor current can be expressed as i(t)cos(10 t _ 8 ) + B.Determine the values of A and B.

Problem 10.8-9 18 W 3.2H i(t) Vs(t) mF 13 $2 In this circuit the voltage source voltage is Va(t) 25 cos(10 t ) Vand the current source current is i(t) 5.0 A_ The inductor current can be expressed as i(t) cos(10 t _ 8 ) + B. Determine the values of A and B.



Answers

Calculate the current in the inductor shown in Fig. P8.9 if the voltage input is (a) $v_{1}(t)=10 \cos \left(377 t+45^{\circ}\right) \mathrm{V}$ (b) $v_{2}(t)=5 \sin \left(377 t-90^{\circ}\right) \mathrm{V}$ Give the answers in both the time and frequency domains.

Hi and given problem current passing through in doctor that is varying as a function of time and it is given as I is equal to five plus 16 ft voltage across this. In victories we are is equal to then millie volt voltage induced. So in the first part of the problem using the expression for the EMF induced across an in DR which has given us all times of D I by DT time derivative of the function of current. So for MF India as we know this is real means this is 10 million walter turn into 10 days par minus three volts is equal to help which we have to find self induct tense and then differentiation of I which is 55 plus 16 ft. So here it will be zero plus 16. The differentiation of five plus 16 T. So finally it will come out to be 16 L. And hence an expression for self inducted. Its will be and they should par minus two invited by 16 means it can also be read in a 6.25 into 10 dish. The power minus four Henry or 0.625 into tended bar minus three Henry. Or finally this is 0.625 millie Henry which is the answer for the first part of this problem. Value of the self independence of the call. No, the second part of the problem we have to find and energy stored in this industry at a time equals to one second time. Given here is one second. And an expression for the energies for magnetic energies for in the conductor is U. Is equal to of L. I square. So for all this is zero point 6 to 5 million Henry or 0.625 into tennis part minus three. Henry multiplied by square of current and current is five plus 16 in 21 at the time given here is one second and having a square of it. So finally this current this energy here will come out to be 0.1 We jules which becomes one of the answer for the second part of this problem. Now in the same second part of the problem we have to find Father means the energy consumed within this energy store in this industry. Quite unique time which is actually the power that will be given by D. You by DT means here using the function for this energy this is differentiation or we can save time derivative of. Uh huh. Into L. Into why plus 16 P. To the whole square taking the constant turns out which includes have and L. No. The differentiation of five plus 6, 20 square first of all. This will be two times of five plus 16. Then differentiation of terms included within the bracket. For the differentiation of 50 for the differentiation of 16 T this is 16 only, so it will be come out to be cancelling this too. This is L into 16 into five plus 16 into one as the time given here is one second. So finally this power here themselves to be zero 0.21 jules per second, which is the second answer for the second part of a given problem. Thank you.

And that tends to be complete pipe many hundreds correct. Is zero 40s less than Europe and it is to be Turn into 1- explanation of -1 medium pier four is greater than you potentially across the introductory is defined as hey do you know you're on duty was quite potential will be zero what is less than you? And potential will be From 5 to 10 to the power -3 and to get over the radio, 10 into 10 to depart ministry 1- Explanation of- Dick. It is to be 250 include 10 24 -6 explanation of minus people. So potential will be Jiro for he is less than europe and 2 15 to 10 20 power minus six explanation of dynasty what he is greater than you be part energy store is half and I is quite So it is zero what he is less than you and it is equal to Contains five into trying to keep our ministry 10 into 10 to dip our ministry 1- explanation of -2 fully support. So it has to be equal to 1250 10 to the four minutes, nine 1- Explanation of-. Mhm. That so, thanks for watching it.

Hi everyone here it is giving through the induct er of independence 25 million Henry current is changing with time has given It is to be zero fine Time to be less than zero. It is to be turned into 1- explanation of- T. For he should be greater than europe. We have to fight potential and uh huh. Energy stored in the in doctor as a function of time. Mhm. The first part we are solving what an insult is to find us. And do you are you conducting? What? Time to be less than ju what the ancient very weak can you fight and to depart ministry Be over duty of zero. So it will be zero and thought Time greater than zero potential difference across the and doctor you can calculate Using the equation one it is to be point to fight explanation of minus stick. Simplifying it potential you will get why to fight explanation of ministry. No energy energy store. In the end dr is to find us half and a square so far Is less than zero. Energy store zero and thought He is greater than zero energy storage building well from 25 into 10 to the Power Ministry into 125 explanation of dynasty You will get 1.25. Thank you. 1- Explanation of Dynasty Holy Square. Yeah, that will be my project. This will be mislabeled. Thanks for watching it.

In this question? Um, yeah. Looking at the rotation across 75 Micro Henry in Dr. Okay, so given a 75 million Henry off Micro Henry. Dr. And they were given the, uh, equation. He The rotation across the conductor is 25. Co sign six p. T. Okay, so we want to calculate the rotation across and dr sometime inductive reactions and the peak current. Okay, so to do part A, um, it's he equals to 0.10 seconds. Okay, the footage is, uh, 25 co sign 60 times 0.1. This is 25 25 who star in six. Okay. And you calculate this, you get 24 words. Okay? So when you calculate this calculate who signed six in region mood. Okay, remember to set your calculator and radio mood to do this calculation. Okay, cause in six degree doesn't make sense. So in this case, the six refers to six regions. Okay. All right. So, uh, a the answer is 24 words and then probably be you are interested in the inductive reactions. So inductive, reactant excel is, uh tau pi f l. Okay, so on our V l is, uh, gen. The general formula is like this. We are times. Uh oh. Sorry. Two pi f p. And this is equal to 25 co sign 60 t. Okay, so that means our two pf is he going to 16? Okay, so explain our Yes. Ah, two pi f l This is 60 times 75 micro. Henry. Uh huh. So you get 4.5. Ah, mealy whom? He So this is the answer for Part B and then Patsy, you want to find a peak current here, the peak current and you calculate using the peak voltage divide by the conductive reactant. So 25 divided by 4.5 times 10 to the negative tree. You get 5600 and peers. Uh huh. So this is the answer for Patsy, and that's all


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