Answer to Question #88945 in Electric Circuits for adam walker

Question

if a piezoelectric structure generates 150 volts and 80 milliwatts with net energy transfers of 2 millijoules per compression how many compressions would be required to charge a 4.4kWh Li-ion battery? Or put another way - if the compression occurred at a rate of 10 per second how long would it take to charge such a battery?

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Answer 1

Convert energy in kWh to energy in joules (J)

$$4.4kWh=4.4\cdot 1000W\cdot 3600s=1.584\cdot {{10}^{7}}J$$

Energy transferred per a compression is

$$2mJ=2\cdot {{10}^{-3}}J$$

To obtain the number of compressions we need to divide the required total energy by the energy of one compression:

$$n=\frac{1.584\cdot {{10}^{7}}J}{2\cdot {{10}^{-3}}J}=7.92\cdot {{10}^{9}}$$

To obtain the time needed to charge the battery to required energy we divide the number of compressions by the rate of the compressions:

$$t=\frac{7.92\cdot {{10}^{9}}}{10\text{ }per\text{ }second}=7.92\cdot {{10}^{8}}seconds$$

Express this time in hours

$$t=\frac{7.92\cdot {{10}^{8}}seconds}{3600\,seconds/hour}=2.2\cdot {{10}^{5}}hours$$

Express this time in days

$$t=\frac{2.2\cdot {{10}^{5}}howers}{24\,howers/day}\approx 9.17\cdot {{10}^{3}}days$$

Express this time in years

$$t=\frac{9.17\cdot {{10}^{3}}days}{365\,days/year}\approx 25\,years$$

So, to charge the battery to 4.4kWh it is required $7.92\cdot {{10}^{9}}$ compressions of piezoelectric structure. The time needed to charge the battery to required energy is

$$7.92\cdot {{10}^{8}}seconds=2.2\cdot {{10}^{5}}hours\approx 9.17\cdot {{10}^{3}}days\approx 25\,years$$