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We have been given a capacitor with dielectrics of constants $k_1, k_2, k_3$ as depicted. The equivalent capacitance of the capacitor is to be calculated.

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Well, according to what i understood, the circuit may be redrawn as follows :

enter image description here

But i was told that such an arrangement would give a wrong answer. The reason for which I cannot understand as the potential difference must be the same across those equivalent capacitors, thus must be in parallel?

Moreover i was told that the correct circuit would be:

enter image description here

Why should i redraw the circuit this way? What am i missing?

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You are wrong, you advisers are correct.

You are assuming that the interface between the three dielectrics is an equi-potential surface. This is not in general true for dielectrics. It would be true if there were a layer of conducting material placed at the interface.

The potential at the interface will be different on the left and right sides because the combination of dielectrics is different. Close to the junction of $k_2, k_3$ there will ideally be a sudden discontinuous change in potential over no distance at all, resulting in an infinitely high electric field. In practice this change will occur smoothly over a finite distance. However, this region will be small under the usual assumptions that the length of the plates is much larger than the distance between them.

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  • $\begingroup$ How your post answers the question ? Your explanation is too much tough. Can you please explain more simply? Also, in the initial problem, there are two principal plates( the plates of capacitors) and four dielectric plates, so how does conservation of mass is failed and new plates are generated in circuit diagrams? $\endgroup$
    – user326901
    Commented Jul 21, 2022 at 12:44

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