# How to calculate total power generated?

I have a circuit with a piezoelectric transducer which converts mechanical energy to electrical. The ceramic is connected to a 1 Megaohm resistor and a voltmeter which reads voltage.

If I want to determine the power generated, do I just use P=V^2/R? And if so, how do I account for fluctuating voltage values? For example: I have the actual values of the voltages on a separate data table. How do I determine total power generated if voltage values are not the same? Do I do summation of power? Essentially, which voltage values do I choose to determine power?

Thank you very much! I appreciate it!

• Don't you mean total energy generated instead of power? Asking for the total power generated is like asking for the total velocity in a trip, it does not make much sense. Instead you can ask for the average velocity, or average power in your case. Or you can ask for the total energy spent by your circuit, which will be the integral of power over time. Mar 15, 2019 at 19:34

If you have the voltage and time data pairs $$(t, V(t))$$ separated by a constant interval of time, eg:

$$(t_0,V_0), (t_0 +h=t_1,V_1), (t_0+2h=t_2,V_2)$$

You can use the trapezoidal rule to obtain the numerical value of:

$$\int_{t_0}^{t_f} V(t) \approx \dfrac{h}{2}(V(t_0)+2 \sum_{k=0}^{N-1} V(t_i)+V(t_n )),$$ $$h=\dfrac{t_f-t_0}{N}, N=$$your number of data pairs.

The mean value of V(t) is:

$$\bar{V}=\dfrac{1}{t_f-t_0}\int_0^{t_f} V(t)$$

Finally your mean value of P(t) is

$$\bar{P}=\dfrac{\bar{V}^2}{R}$$

$$P=IV$$ And subsequently $$P = \frac{V^2}{R}$$ Represents the total rate at which work is being done on electrons by an electric field, within a region undergoing a potential drop V at time t

As such, the fact that the potential drop is variable, means that the rate at which work is being done on electrons by the electric field is changing with time. Meaning that the power( energy/second) that your component is using, depends on the time you measure it.

Energy:

The notion of "total power" as the sum of these powers, doesn't make sense. I think the quantity that you actually want to calculate, is the total energy that is being transfered to the electrons by the electric field in time t

By definition $$P = \frac{dw}{dt}$$

$$W = \int_{0}^{t} P dt$$

$$W = \int_{0}^{t} \frac{V^2}{R} dt$$