Rotating Capacitor and a Transient Electric Network

Abstract

This paper presents a rotating parallel-plate capacitor; one of the plates is assumed to turn about the common vertical axis through the centers of the square plates. Viewing the problem from a purely geometrical point of view, we evaluate the overlapping area of the plates as a function of the rotated angle. We then envision the rotation as being a mechanical continuous process. We consider two different rotation mechanisms: a uniform rotation with a constant angular velocity and, a rotation with a constant angular acceleration—we then evaluate the overlapping area as a continuous function of time. From the electrostatic point of view, the time-dependent overlapping area of the plates implies a time-dependent capacitor. Such a variable, a time-dependent capacitor has never been reported in literature. We insert this capacitor into a series with a resistor, forming a RC circuit. We analyze the characteristics of charging and discharging scenarios on two different parallel tracks. On the first track we drive the circuit with a DC power sup-ply. We study the implications of the rotation modes. We compare the response of each case to the corresponding tradi-tional constant capacitor of an equivalent RC circuit; the quantified results are intuitively just. On the second track, we drive the circuit with an AC source. Similar to the analysis of the first track, we generate the relevant electrical characteristics. In the latter case, we also analyze the sensitivity of the response of the circuit with respect to the fre-quency of the source. The analyses of the circuits encounter nontrivial differential equations. We utilize Mathematica [1] to solve these equations.

This paper presents a rotating parallel-plate capacitor; one of the plates is assumed to turn about the common vertical axis through the centers of the square plates. Viewing the problem from a purely geometrical point of view, we evaluate the overlapping area of the plates as a function of the rotated angle. We then envision the rotation as being a mechanical continuous process. We consider two different rotation mechanisms: a uniform rotation with a constant angular velocity and, a rotation with a constant angular acceleration—we then evaluate the overlapping area as a continuous function of time. From the electrostatic point of view, the time-dependent overlapping area of the plates implies a time-dependent capacitor. Such a variable, a time-dependent capacitor has never been reported in literature. We insert this capacitor into a series with a resistor, forming a RC circuit. We analyze the characteristics of charging and discharging scenarios on two different parallel tracks. On the first track we drive the circuit with a DC power sup-ply. We study the implications of the rotation modes. We compare the response of each case to the corresponding tradi-tional constant capacitor of an equivalent RC circuit; the quantified results are intuitively just. On the second track, we drive the circuit with an AC source. Similar to the analysis of the first track, we generate the relevant electrical characteristics. In the latter case, we also analyze the sensitivity of the response of the circuit with respect to the fre-quency of the source. The analyses of the circuits encounter nontrivial differential equations. We utilize Mathematica [1] to solve these equations.

Cite this paper

nullH. SARAFIAN and N. SARAFIAN, "Rotating Capacitor and a Transient Electric Network,"*Journal of Electromagnetic Analysis and Applications*, Vol. 1 No. 3, 2009, pp. 138-144. doi: 10.4236/jemaa.2009.13022.

nullH. SARAFIAN and N. SARAFIAN, "Rotating Capacitor and a Transient Electric Network,"

References

[1] S. Wolfram, “The mathematica book,” 5th Ed., Cambridge University Publication, 2003.

[2]
D. Halliday, R. Resnick, and J. Walker, “Fundamentals of physics extended,” 8th Ed, John Wiley and Sons, 2007; J. D. Jackson, “Classical Electrodynamics”, 3rd Ed, John Wiley and Sons, 1998.

[3]
M. Trott, “The mathematica guidebook for graphics,” Springer, 2004.

[4]
H. Sarafian, “Rotating rectangular parallel-plate capacitor and a transient electric circuit”, International Mathematica Symposium, IMS, 2008.

[5]
H. Sarafian, “Rotating elliptical parallel-plate capacitor and a transient electric circuit”, International Conference on Computational Science and its Application, ICCSA’08, pp. 291–296, Springer 2008.