Hi everyone. We continue with our series when we learn about the capacitors and inductors. And in this video, we introduce the physics of the inductor, current-voltage relationship of the inductor, and the energy stored in an inductor. So the inductor is an electric component that is used to store energy in form of magnetic flux. And the basic idea behind the inductance is that if I have a wire and I have a current going through this wire, then there would be a magnetic field or a magnetic flux around this wire. Even more, if I turn this wire and wound it and have a coil that look like this shape here, and then I pass a current through this coil, then there will be a magnetic flux that resemble a permanent magnet bar. So here we have a magnetic flux. This configuration here makes a coil, and this coil we call it as an inductor. The inductance of this inductor quantify the ability of the inductor to store energy in a form of a magnetic field. So the inductance is measured in Henry, and the inductance or the capacity to store this magnetic field depend on the permeability of the core like the material within the coil, the physical construction of the coil like length, the cross-sectional area, and the number of turns. So in physics, we have seen this equation. The inductance depend on the number of turns, the cross-sectional area A, and μ the permeability of the core material, and inversely proportional to the length of our wire.

So now current is going through the coil that has an inductance L. There will be a magnetic flux around the coil. This magnetic flux is linearly proportional to the current I through a proportionality constant which is the inductance L. Now if I vary the current through the inductor, the flux will also vary accordingly. So dΦ where Φ is the flux is equal to L*di. Now if I take the derivative of this equation with respect to time, I have dΦ/dt = di/dt * L. Now if you remember from early the semester, dΦ/dt the rate of a change of flux will actually induce voltage. So V the voltage across the inductor is equal to L dI_L/dt where I_L here is the current through the inductor. And integrating this equation, I can write that I the current through the inductor is equal to 1/L integral of V*dt with V here as the voltage across that inductor. So we just derived an equation for the voltage, the current-voltage relationship for the inductor.

So here is our circuit symbol for the inductor. It has inductance L and I have a current going through it. With the current go through it, we going to have induced magnetic field, and this flux here is proportional to the current. If the current varies, the flux vary, and if the flux vary, we're going to have a voltage or induced voltage across this inductor. So if you'd like to consider or compute the power of that inductor, power is in general equal to I * V. So we can write it in terms of the inductor's current so I and then V would be replaced by L*dI/dt. Now if I'd like to consider the energy stored in that inductor, I know that the energy is P * T or the rate of change of energy is equal to P * dt. So I have dw = L*d i * i. Now to get the energy, I need to integrate this equation. So now I have w equal to the integral of id iL. This give me 1/2Li². Okay, so this would be the amount of energy stored in an inductor. And please be reminded that the inductor store energy in form of a magnetic field.

So let's practice this simple equation here. So I have a network that has inductors and resistors. I have a supply current here that is equal to 600 milliamp, and I know that the energy stored in L1 is 28 Joules, and we'd like to compute the total energy stored in the second inductor L2. Okay, so to get the energy in the inductor L2, so W2 is equal to 1/2L2I2^2. So basically I need to get this current I2. Okay, I don't have I2 instead I have the total current supplying the circuit. I also have the energy in L1. If I have the energy in L1, I can solve for the current I1, the current through the inductor one. And once I have the current in inductor 1, we can write a KCL here such that the total current N which is 6 milliamp equal to I1 + I2. We can solve for I1 using the energy stored in I1 in inductor one. So now we can get I2 as 600 milliamp minus I1. Okay, so here we compute I1 from the energy and solve for I for I2. Once I have I2, the energy will equal to 1/2* L2* I2². We substitute the numbers here and we end up having 3 mJ.

So in this video we learn about our inductor briefly. So the inductor has a symbol. It is a coil of wounded wire. It has a capacitance L. This capacitance L depend on the physical construction of our coil. The once we have a current through the inductor, we're going to have a magnetic field around this inductor. The flux is equal to L the inductance time I the current. Taking the d of this equation with respect to time give us v = L di/dt and equivalently can write down that i is equal to 1/L integral of v dt. And the energy stored in an inductor is stored in the form of a magnetic field and is equal to 1/2 L i². So basically this is the main takeaway of the physics from the physics of the inductor. Thank you so much for listening.