JAMP  Vol.8 No.1 , January 2020
Theoretical and Experimental Analysis of Energy in Charging a Capacitor by Step-Wise Potential
Abstract: In this paper, charging capacitor in RC circuit, to a final voltage, via arbitrary number of steps, is investigated and analyzed both theoretically and experimentally. The obtained results show that the stored energy in the capacitor is constant independent of N, but the dissipated energy in the resistor and the consumed energy by the power supply decreases as number of steps N increases (adiabatic charging). The limit when the step number goes to infinity is examined and our result shows that the dissipated energy vanishes theoretically. This limit is carried out experimentally by using a ramp potential.
Cite this paper: Al-Jaber, S. and Saadeddin, I. (2020) Theoretical and Experimental Analysis of Energy in Charging a Capacitor by Step-Wise Potential. Journal of Applied Mathematics and Physics, 8, 38-52. doi: 10.4236/jamp.2020.81004.

[1]   Bezryadin, A., Belkin, A., Llin, E., Pak, M., Colla, E. and Huber, A. (2017) Large Energy Storage Efficiency of the Dielectric Layer of Graphene Nanocapacitors. Nanotechnology, 28, Article ID: 495401.

[2]   Asnawi, R., Nurhadiyanto, A.Z. and Asmara, A. (2018) The Characteristic of Supercapacitors Circuit as a Future Energy Storage Media. Journal of Physics: Conference Series, 1140, Article ID: 012001.

[3]   Fletcher, N.H., Hilton, A.D. and Ricketts, B.W. (1996) Optimization of Energy Storage Density in Ceramic Capacitors. Journal of Physics D: Applied Physics, 29, 253-258.

[4]   AL-Jaber, S.M. and Salih, S.K. (2000) Energy Consideration in the Two Capacitor Problem. European Journal of Physics, 21, 341-345.

[5]   Makihara, K., Onoda, J. and Miyakawa, A. (2006) Low Energy Dissipation Electric Circuit for Energy Harvesting. Smart Materials and Structures, 15, 1493-1498.

[6]   Newburgh, R. (2005) Two Theorems on Dissipative Energy Losses in Capacitor Systems. Physics Education, 40, 370-372.

[7]   Kahn, M. (1998) Capacitors and Energy Losses. Physics Education, 23, 36-37.

[8]   Wang, D. (2017) The Most Energy Efficient Way to Charge the Capacitor in a RC Circuit. Physics Education, 52, Article ID: 065019.

[9]   Lee, M. and Kim, J. (2016) Design of a 93% Energy-Efficient Buck-Type Capacitor Charger IC in 250-nm CMOS. IEEE Transactions on Industry Applications, 52, 3203-3211.

[10]   Shah, A.S., Arslan, S. and Kim, H. (2018) A Reconfigurable Voltage Converter with Split-Capacitor Charging and Energy Recycling for Ultra-Low-Power Applications. IEEE Access, 6, 68311-68323.

[11]   Batygin, K. and Stevenson, D.J. (2010) Inflating Hot Jupiters with Ohmic Dissipation. The Astrophysical Journal Letters, 714, L238-L243.

[12]   Roy, K. (2014) Ultra-Low Energy Computing Paradigm Using Giant Spin Hall Devices. Journal of Physics D: Applied Physics, 47, Article ID: 422001.

[13]   Plunk, G.G., Tatsuno, T. and Dorland, W. (2012) Considering Fluctuation Energy as a Measure of Gyrokinetic Turbulence. New Journal of Physics, 14, Article ID: 103030.

[14]   Palaniselyam, T. and Baek, J. (2015) Graphene Based 2D-Materials for Supercapacitors. 2D Materials, 2, Article ID: 032002.

[15]   Bagheri, S., Wu, N. and Filizadeh, S. (2018) Modeling of Capacitor Charging Dynamics in an Energy Harvesting System Considering Accurate Electromechanical Coupling Effects. Smart Materials and Structures, 27, Article ID: 065026.

[16]   Shah, R., Zhang, X. and Talapatra, S. (2009) Electrochemical Double Layer Capacitor Eectrodes Using Aligned Carbon Nanotubes Grown Directly on Metals. Nanotechnology, 20, Article ID: 295202.

[17]   Tran, C.D., Vu, A.Q. and Van, L.T. (2018) Uniform Coating of Polyaniline on Porous Carbon Nanofibers as Efficient Electrodes for Supercapacitors. Journal of Physics: Conference Series, 1082, Article ID: 012081.

[18]   Boechler, G.P., Whitney, J.M., Lent, C.S., Orlov, A.O. and Snider, G.L. (2010) Fundamental Limits of Energy Dissipation in Charge-Base Computing. Applied Physics Letters, 97, Article ID: 103502.

[19]   Pasha, M.S. and Prabhakar, G.C. (2015) Micro Controller Based Energy Efficient Four Steps Charging of a Capacitor Using a Buck Converter with Consecutive Changes of its Duty Ratio. International Journal of Engineering Trends and Technology, 27, 89-93.

[20]   Savitha, S. M., Rajani, H. P/ and Hunagund, S. M. (2018) Implementation of Low Power Adiabatic SRAM. International Journal of VLSI Design & Communication Systems, 9, 1-18.

[21]   Nakata, S. and Katagiri, Y. (2007) Electrostatic Energy, Potential Energy, and Energy Dissipation for a Width-Variable Capacitor System during Adiabatic Charging. Journal of Applied Physics, 101, Article ID: 034911.