When I was a JEE aspirant, questions like these were nightmares for me. Now I am almost through my first year at IIT Kharagpur. After studying the subject Electrical Technology, these have become beginner level problems. 😅 And if any JEE aspirant is reading this, after joining college, you'll have the same transition as me. From nightmare to one of the simplest practice problems.
Taking a first stab. Happy to receive corrections. A) At DC (omega=0) the inductor presents zero impedance and the capacitor, infinite. Thus there is no DC component to the current through C. The AC current through the capacitor would then simplify to V_2 / (X_L - X_C) at the same frequency as the input since X_L is greater than X_C (and no R); the phasor points straight up. The current leads voltage by 90 degrees. B) The output voltage is directly across the capacitor, which has an an instantaneous value of Q/C. The charge on the capacitor comes from that provided by the DC input V_1 in a superposition with that of that provided by the AC input. Thus the output component attributable to the AC input is (Q/C) - V_1. Overall output voltage is superposition of V_1 + (V_2 * attenuation_factor described in the next answer) at the same frequency as the input, and will be essentially in phase with the AC component of the input. C) If you think of it as a voltage divider, with A and B, measuring across B, the normal voltage divider formula B/(A+B) applies and describes the ratio of AC output voltage to AC input voltage-- specifically X_C / (X_L + X_C), a ratio that will grow arbitrarily small (greatest attenuation) as X_L dominates.
In lecture 25 of 8.02, Walter Lewin derives the differential equation for a driven LRC circuit and solves for current I. I = V₁·cos(ωt - 𝜑)/√[R² + (ωL - 1/ωC)²] where tan 𝜑 = (ωL - 1/ωC)/R V₁·cos ωt is the input voltage, Vᵢ(t). R can be the internal resistance of the voltage supply. In problem #197 we set R = 0. ωL > 1/ωC => tan 𝜑 -> +∞ => 𝜑 = 90° cos(ωt - 90°) = sin ωt => Answer (a): I = V₁·sin (ωt)/(ωL - 1/ωC) 𝜑 = 90° (b) V₀(t) = Q(t)/C jω method => V₀(t) = (1/jωC)/[(1/jωC) + jωL]·V₁(t) => V₀(t) = 1/(1- ω²LC)· Vᵢ·cos(ωt) Answer (b): Amplitude = Vᵢ/(1- ω²LC) = Vᵢ/[1- (ω/ω₀)²] The phase is zero at low frequencies. (c) V₀(t) = XC/[XC + XL]·V₁(t) XC XC/[XC + XL] -> XC/XL Answer (c): The amplitude goes to XC/XL Since XC
Hello Ulf - I have already recorded this early afternoon the solution to 197. I will post it on April 11. I mention the 5 viewers with the correct solution. I mentioned YOU and said that I had not seen a solution from you which surprised me. *I do not want to redo the video. Please accept my apologies.*
@@lecturesbywalterlewin.they9259 Hello dr Lewin. It is perfectly fine for me! 🙂 I got very little time to do this problem. In the weekend and before it was terrible weather here in Sweden. It was snowstorm and hard to be out on the roads, and I was on a travel. Very slippery when the temperature went below 0 deg, C. When I came home in the beginning of the week there was suddenly a weather change with summer temperatures up to +20C. I saw that you had posted a new problem but the weather was too fine to be indoors. I started to look at the problem on tuesday and I must admit that I had some problems with the solution even if I thought I knew everything about these kind of circuits. I was not sure what exactly the question was in some cases. But I had written something anyway and decided to post yesterday night. Good to hear from you and hope you are fine! Regards /Ulf
I just re-watched 8.02 25 and... was MIT really at 110V AC? I'm on the west coast and we've been at 120V for over 100 years and I was always taught that the US is 120V and Japan in 110V, and equipment is rated at 110V to indicate that it will also work in Japan (with the actual specification normall 110-130V since it was usually designed for 120V)
Mains voltage in Japan is nominally 100V. U.S. is 110-120. In many homes you will find it is on the high end of this range or even higher. U.S. TV sets from the 1950s often are labeled 117 V, which apparently was the nominal voltage used for testing the power draw.
The utility (NSTAR at the time of that lecture) has a standard to maintain mains voltage at the service point within 5% of nominal, which the US has had at 120V for a long time. Mains voltage is a moving target, because it depends on the behavior of other customers on your part of the network, and how the utilities adapt to it. This means the mains voltage that's supposed to be 120V could start at 115V (very common during the daytime), and through the voltage drop along the path from the service point to the load receptacle, it could drop as low as 110V. Likely, MIT has a campus distribution grid, and customer-owned transformers for each building, so NSTAR wouldn't be responsible for controlling all the transformer taps, but rather the facilities maintenance staff would. Likely, they have medium voltage distribution, and a master 480V transformer for each large building to run the big ticket loads. Small loads like receptacles, are powered by smaller 480V:120/208V transformers.
@@lecturesbywalterlewin.they9259 Spent the whole afternoon professor - couldn't do it. Totally stumped by the question of separating the capacitor from the self inductor relative to the formulaic solution of the total current(I) provided in lecture 25... Differentiating between the resonance for maximum values and it's practical application also had me in a knot even though not sure if it is required. "Gemini"(Google's AI)(It is possible to upload images for it to analyze...) says the initial amplitude would be 20( V20*sin(Wt)) but I'm not sure how that changes... and the phase I'm guessing would be the difference between the current and voltage after the transformation... At least I saw that the voltage would be leading the current while comparing the information* Will keep trying as you post Professor🙏🙏(trying to save my life* trading so the struggle is real atm)
If i consider the AC LC-circuit with V2 = V20 * sin(w*t) and Q2 / C = AC-component of the Output Voltage, i get the differential equation ( for R = 0 ): L * d²Q2 / dt² + Q2 / C = V20 * sin(w*t) with the solution for the current I(t) = - V20 / (XL - XC) * cos(w*t), with XL = w * L (reactance of the selfinductor) and XC = 1 / (w*C) (reactance of the capacitor). Q2(t) = - 1 / w * V20 / (XL - XC) * sin(w*t) it is integration for I(t) with the starting condition Q2(0) = 0. d²Q2 / dt² = w * V20 / (XL - XC) * sin(w*t) you can verify this by inserting this in the differential equation above. a) A DC voltage does not produce a significant current in the capacitor after the capacitor is as well as charged. The AC-component V2 leads to the above current I(t) = - V20 / (XL - XC) * cos(w*t) with the amplitude Imax = V20 / (XL - XC) . b) V2out = Q2 / C = - XC / (XL - XC) * V20 * sin(w*t) with the amplitude XC / (XL - XC) * V20. c) If i write for XL = n * XC with a large number n i get: V2out = - XC / (XL - XC) * V2 = - XC * V2 / ( XC * (n - 1) ) = V2 / ( n - 1 )
Mass is the amount of matter contained in a body or an object meanwhile weight is total mass multiplied by acceleration due to gravity which we commonly refer to as weight. Weight varies therefore place to place. I believe that should be enough.
Apply to MIT. If they accept you, to get a bachelor's degree at MIT takes 4 years (about 25 courses). Both 8.01 and 8.02 are GIRs (general institue requirements). They may give you credit for 8.01 and 8.02 if you pass a special test made for students who have already covered 8.01 and 8.02.
Hi Prof. Could you please help us to know the solution of this problem. On internet there is conflict in solution. The problem is-In a pond, there is a ship floating with a large rock on board. If the rock is removed from the ship and dropped into the pond, will the water level of the pond increase, decrease, or remain the same?
Sir please answer this ques from the topic electric flux - A charge q is placed inside a cube at a distance d from one of the corners of the cube. What will be the electric flux through each face of the cube due to the charge q?
Lookup Coulomb's law & Gauss's flux theorem. Both in WL's lectures. Also, how far away is it from at least one of the other corners or some other reference? 1 reference point relative the charge is not enough to work out how big the cube is and how big its sides are, how close they are, and so on... Proportions? 2 independent angles to go with that distance would also be handy, then you have a 3d vector in the cube.
I have an experiment for you: Suppose you have a closed circuit with a car battery and a lamp. Consider that it is an ideal battery with an internal resistance zero (you can think of parallel conection of 100 000 000 car batteries). Now i put this battery in a black box, so that you can only see the plus and minus contacts. I have the possibility of replacing this battery with a superconducting coil with a linear increasing magnet field inside the coil, so that you get the same DC output voltage. If the battery is inside the blackbox powersupply you would say the path integral E ds over the blackbox powersupply is -V. If the coil would be inside the blackbox powersupply, you claim, that the path integral E ds over the blackbox powersupply is zero. How can you figure out if you should write -V or zero without opening the box ? PS: I by myself would say that the induction coil produces an induction voltage Ui = - L * dI / dt = -V and I would say I don't care what's in there.
But you do care what is in there because you know. That is why you put Ui = - L * dI / dt = -V. I dont know, so it is just a power supply with a voltage across its terminals. If I lived inside the black box I would do Faraday around an internal loop where the outside is an unknown load, with a voltage across it and drawing some current.
"Hey, I hear you think randomness is a major force in the universe. You're right, randomness plays a huge role in many things around us. But here's something cool - sometimes, completely random events can create super complex systems. Like, snowflakes - those beautiful patterns come from random water molecules freezing together. Or the amazing variety of life on Earth, that's all thanks to billions of random mutations. "Now, think about the whole universe itself. Lots of scientists believe the basic laws of physics are like perfectly set dials for life to exist. Even the tiniest change and things could be completely different, no life at all. This fine-tuning, as they call it, is a big mystery. Randomness alone might not be the whole story. "That's where the idea of God comes in for some people. Maybe this fine-tuning points to some kind of intelligence behind it all, someone who set these laws in motion. It doesn't get rid of randomness, but it offers another way to think about it. "In the end, whether you believe in God or not, the universe is still an amazing and mysterious place. Maybe the beauty of randomness and the possibility of a deeper plan are both parts of this incredible existence." All of the history tells that the Quran is a very old book so how someone could mention scientific facts as signs in it that are known recently. Obviously it's gods word in which you can never find any mistake but can find new facts that are still not known
evolution through natural selection is *NOT random.* 4 billion years ago the Earth was loaded with living single cells. 2 billion years ago there was already advanced life of 2 single cells. From that day on Evolution occurred by Natural Selection and tens of millions of animals evolved (many of them are now extinct because of the Natural Selection) of which homo sapiens was 1 and they probably evolved the way we know humans now. We too may become extinct because of natural selection. The quran and the bible were both written by people out of fear. *Fear for death in the first place that's why after life was invented by people* .
My respect professor I reread the Quran with your word to see how is it really we created God out of fear but guess what now l believe in God more now look at these verse in surah Al-Hajj verse 5 O People, if you should be in doubt about the Resurrection, then [consider that] indeed, We created you from dust, then from a sperm-drop, then from a clinging clot, and then from a lump of flesh, formed and unformed - that We may show you. And We settle in the wombs whom We will for a specified term, then We bring you out as a child, and then [We develop you] that you may reach your [time of] maturity. And among you is he who is taken in [early] death, and among you is he who is returned to the most decrepit [old] age so that he knows, after [once having] knowledge, nothing. And you see the earth barren, but when We send down upon it rain, it quivers and swells and grows [something] of every beautiful Did Mohammed had X ray To see the fetus being created in its mother’s womb Or he a seismologist needed to know that falling water causes earthquakes, a very recent discovery Only who created us in our mother's womb and created the earth will know that
4 billion years ago the Earth was loaded with living single cells. 2 billion years ago there was already advanced life of 2 single cells. From that day on Evolution occurred by Natural Selection and tens of millions of animals evolved (many of them are now extinct because of the Natural Selection) of which homo sapiens was 1 and they evolved into humans the way we know them now. We too may become extinct because of natural selection. The quran and the bible were both written by people out of fear. *Fear for death in the first place that's why after life was invented by people*
You and the rest of humanity would be much better off by relying on reason, evidence, science, logic, and empathy for your guide through life instead of a bronze aged manuscript of dubious origin.
