Power from piezo material

Question

Suppose there is a given piezoelectric material and under a given force it produces voltage $V$. If an external electric circuit is attached with load $R$, the current will be $I= V/R$. Also power generated will be $V^2/R$. By choosing $R$ very low, high energy can be obtained. Is this understanding correct?

Answer 1

This is wrong for at least two reasons.

First, if you apply a constant force to the piezoelectric material, you will produce a voltage across it but no current will flow. You can only generate a current by doing mechanical work on the material. That means you only get a current while you are changing the force, and therefore changing the amount that the material bends or stretches.

Second, you are ignoring the internal electrical impedance of the material. If the impedance was a constant resistance, it is fairly easy to show that the maximum power in the load occurs when the load $R$ is the same as the internal resistance. See the Maximum Power Transfer theorem. If $R$ is smaller than this, most of the power is "wasted" within the piezo material instead of being transferred to the load. If $R$ is bigger, the higher impedance of the complete circuit reduces the power that is generated, in a similar way to your attempt at analysing what happens using Ohm's law.

The same idea applies to a piezoelectric material, but the internal impedance is more like a capacitance than a resistance, so you need to analyze the behaviour of the circuit for an alternating current, and the amount of power transferred depends on the frequency of the force applied to the material, as well as on the internal and load impedances. Basically, you get more power by moving the piezo material faster.