Battery knowledge · Transport and modelling
RC pair
A resistor and capacitor in parallel, the building block of an equivalent circuit model. Each pair reproduces one time constant of the cell’s voltage response, from the seconds of charge transfer to the minutes of diffusion. [1]
- Also called
- RC element, RC branch
- Relationship
- τ = R × C
Example
Calculate a response time
An illustrative 0.02 Ω resistance and 500 F capacitance have τ = RC = 10 s. A first-order step response reaches about 63% of its final change after one time constant.
Explore the graph
One time constant completes about 63% of a first-order voltage change.
At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.
τ = RC; step response = 1 − e^(−t/τ)
Illustrative model. Two separate analytical experiments; normalized voltage, not measured data.
Use in Lemonergy
Lemonergy Studio blocks
Observe an RC time constant
An RC circuit uses source, resistor, capacitor and reference blocks.
Blocks to use
- Controlled voltage source
Applies voltage
Inputs & settings
- voltageV
- Resistor
Sets resistance
Inputs & settings
- resistanceOhm
- Capacitor
Stores charge
Inputs & settings
- capacitanceF
- initialVoltageV
- Electrical reference
Sets zero potential
Inputs & settings
- Connect p to reference net
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
Example. From zero initial voltage with a 1 V step, ideal capacitor voltage is about 0.632 V at 1 s and 0.865 V at 2 s.
Observe. Doubling resistance or capacitance doubles the time constant.
This generic circuit does not identify cell parameters from measurements.
Open the RC example →References & further reading
Technical references
- Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification
Gregory L. Plett · Journal of Power Sources · 2004
Technical reference · Battery charge balance, open-circuit voltage, ohmic loss, polarization dynamics and model identification; parameters require cell-specific data.
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell
Marc Doyle, Thomas F. Fuller, John Newman · Journal of The Electrochemical Society · 1993
Topic background · Porous-electrode transport and insertion-cell modeling; foundational work rather than a specification for a particular commercial cell.
- Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing
IUPAC · 2011
Topic background · Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.