I want to model a coil circuit with induced EMF. I want to verify that my model is correct in a circuit. That the voltage developed across the load is calculated correctly. From the equivalent circuit, you can see the current depend on the jX_L and it acts as a low pass filter in the complete circuit loop because the value increase and cause less voltage develop across the Load.(adsbygoogle = window.adsbygoogle || []).push({});

Let coil:

[tex]Z_L=R_L+jX_L[/tex]

Maxwell eq. For EMF induction:

[tex]\nabla\times \vec E =-\frac {\partial \vec B}{\partial t}\;\Rightarrow\; \int_S \nabla \times \vec E\;\cdot\;d\vec S = \int_C \vec E\cdot d \vec l = -\frac{\partial}{\partial t}\left(\int_S \vec B \cdot d\vec S\right)=-\frac{\partial \Phi}{\partial t}[/tex]

Where [itex]\Phi\;[/itex] is the magnetic flux. Therefore induced EMF:

[tex]V_{IND}= \int_S \nabla \times \vec E\;\cdot\;d\vec S = \int_C \vec E\cdot d \vec l = -\frac{\partial}{\partial t}\left(\int_S \vec B \cdot d\vec S\right)=-\frac{\partial \Phi}{\partial t}[/tex]

To put the whole thing together, using the coil to drive the load, the total equivalent circuit is shown with the [itex]\;V_{IND}\;[/itex] modeled as anideal voltage source:

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where I use [itex]Z_L=R_L+jX_L[/itex] and the current in the loop is:

[tex]I= \frac {V_{IND}}{R_L+jX_L+R_{LOAD}}\;\hbox { and }\; V_{LOAD}=I\;R_{LOAD}[/tex]

I updated that the load is a pure resistance, not reactance, or else it can really get dicey!!

Thanks

Alan

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# Equivalent circuit of induced EMF of coil.

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