Determine the maximum magnetic flux through an inductor connected to a standard outlet (ΔVrms=12

Determine the maximum magnetic flux through an inductor...

Key Concepts

Faraday's Law of Electromagnetic Induction

Faraday's law explains how a changing magnetic flux through a circuit induces an electromotive force (EMF) in that circuit. This principle underpins the operation of inductors, as the induced voltage in an inductor is directly proportional to the rate at which the magnetic flux through it changes over time.

Root-Mean-Square (RMS) Voltage

RMS voltage is used to represent the effective voltage of an alternating current (AC) system. It represents the equivalent steady (DC) voltage that would deliver the same amount of power to a resistive load, and for a sinusoidal waveform, the RMS value is derived from the peak voltage divided by the square root of two.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It quantifies the number of magnetic field lines penetrating the surface, and its value depends on both the strength of the magnetic field and the area through which it passes, as well as the orientation of the field relative to that area.

Sinusoidal AC Waveforms

AC circuits typically operate with sinusoidal waveforms, where the voltage or current varies in a smooth, periodic manner over time. Understanding these waveforms is essential for converting between peak values and RMS values, and for analyzing how these time-varying signals interact with circuit elements like inductors.

Transcript

00:01 In this problem we are asked to find the maximum, let's say this is an inductor, we are asked to find the maximum flux, maximum magnetic flux.

00:14 So i will write a b for magnetic flux.

00:18 Maximum antics flux through this inductor.

00:20 We can write from the definition of a flux that in magnetic flux is given by a number of turns, a cross -sectional area times a b.

00:29 So we'll find a b and substitute the value and they get the maximum main flux through the inductor.

00:36 We can find a b by writing equation for xl first, that is, reactance is equal to 2 pi f times l, where we know that irms is equal to vr -rms divided by xl reactants.

00:55 So if we substitute the value for xl, that is 2 pi, fl here and our i max is i max is equal to square root of two times i rmsm if we substitute the value for i if you write r rm s in terms of i max we can get this is this will be square root of two vrmss divided by 2 pi fl then um we know the magnet field inside the inductor that that is b is equal to mu number of turns times the current passing through inductor maximum divided by l.

01:43 L is the length of the wire or inductor.

01:47 From here, then we can simplify this to mu n times square root of 2 times vr -rms.

01:56 We substituted the value for ir max that we found previously, divided by 2, fl divided by l.

02:07 Our v -no -l will be equal to u -not n squared by times a divided by l.

02:17 So we'll substitute the value for l for an inductor.

02:21 So substituting the value for l, that is, we get here relation for a b will be equal to square root of a 2, mu -nodd n, vrms, divided by 2 pi f, f, times mu nod n square a divided by l times l...

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