# Magnetic field effects in high-power batteries; 2: Time constant of a radial circuit terminated by a cylindrical cell with inductance

## Abstract

The time constant to steady state of an electric signal applied to the outer boundary of a radial circuit that propagates to a centrally located cylindrical conductor is determined rigorously by a transmission-line analysis. Two cases are reported: the perfect radial conductor and a radial conductor with a finite resistance. The time constant is featured as a function of the ratio of the radius of the radial conductive leads to the radius of the inner conductor. As the ratio is increased, the time constant departs from that of an electric field penetrating a cylindrical conductor and approaches the inductive time constant of the leads. An analytic approximation of the time constants of the system also is provided. This analysis should assist in the development of high-power circuitry design when the discharge time is on the order of the inductive time constant.

- Authors:

- (Univ. of California, Berkeley, CA (United States). Materials Science Div.)

- Publication Date:

- OSTI Identifier:
- 7039032

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Journal Article

- Journal Name:
- Journal of the Electrochemical Society; (United States)

- Additional Journal Information:
- Journal Volume: 141:3; Journal ID: ISSN 0013-4651

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 25 ENERGY STORAGE; LEAD-ACID BATTERIES; INDUCTANCE; PERFORMANCE; ELECTRIC FIELDS; MAGNETIC FIELDS; MATHEMATICAL MODELS; STEADY-STATE CONDITIONS; TIME DEPENDENCE; ELECTRIC BATTERIES; ELECTRICAL PROPERTIES; ELECTROCHEMICAL CELLS; PHYSICAL PROPERTIES; 250902* - Energy Storage- Batteries- Performance & Testing

### Citation Formats

```
Battaglia, V., and Newman, J.
```*Magnetic field effects in high-power batteries; 2: Time constant of a radial circuit terminated by a cylindrical cell with inductance*. United States: N. p., 1994.
Web. doi:10.1149/1.2054796.

```
Battaglia, V., & Newman, J.
```*Magnetic field effects in high-power batteries; 2: Time constant of a radial circuit terminated by a cylindrical cell with inductance*. United States. doi:10.1149/1.2054796.

```
Battaglia, V., and Newman, J. Tue .
"Magnetic field effects in high-power batteries; 2: Time constant of a radial circuit terminated by a cylindrical cell with inductance". United States. doi:10.1149/1.2054796.
```

```
@article{osti_7039032,
```

title = {Magnetic field effects in high-power batteries; 2: Time constant of a radial circuit terminated by a cylindrical cell with inductance},

author = {Battaglia, V. and Newman, J.},

abstractNote = {The time constant to steady state of an electric signal applied to the outer boundary of a radial circuit that propagates to a centrally located cylindrical conductor is determined rigorously by a transmission-line analysis. Two cases are reported: the perfect radial conductor and a radial conductor with a finite resistance. The time constant is featured as a function of the ratio of the radius of the radial conductive leads to the radius of the inner conductor. As the ratio is increased, the time constant departs from that of an electric field penetrating a cylindrical conductor and approaches the inductive time constant of the leads. An analytic approximation of the time constants of the system also is provided. This analysis should assist in the development of high-power circuitry design when the discharge time is on the order of the inductive time constant.},

doi = {10.1149/1.2054796},

journal = {Journal of the Electrochemical Society; (United States)},

issn = {0013-4651},

number = ,

volume = 141:3,

place = {United States},

year = {1994},

month = {3}

}