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I am reading about piezoelectric elements and I am not sure why a piezoelectric material is like a capacitor. So a mechanical stres on the material will displace the electric charge distribution creating a potential difference. But current cant flow through ? So why is it a capacitor ?

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Because that is exactly the effect a capacitor gives: It causes current to flow in other parts of the circuit around it due to attraction/repulsion of charges on either side of it - but no current can actually flow through it.

  • In essence, in the piezoelectric element you have an atomic structure of the unit cell which skews the charge distribution towards one side when it is mechanically "squeezed". See this nice illustration from this source:

enter image description here

  • A capacitor on the other hand is "filled up" with charges when connected to a battery or other voltage source. Charges of opposite sign will place themselves on either of the capacitor's plates. Illustration from this source:

enter image description here

The result in both of these is now that you have a positive net charge on one side and a negative net charge on the other, while there is no conducting material in-between through which charge can move. So, current can't flow through them, but they nevertheless are able to drive current as a voltage source because of their net voltage across their oppositely charged sides - much like a battery, albeit their voltages will vary very differently over time.

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