# How to find time constant of battery first order model with unknown capacitance?

The above picture is the first order circuit model of battery. I'm trying to calculate the value of R1 and C1 with specified time varied input and output. In order to calculate that, I have to know the value of time constant first but I have no idea how to calculate that without knowing the value of C1.

• Where did the picture of the circuit come from and what battery was it related to? – Andy aka May 15 at 11:59
• The information you need can probably be calculated from the "specified time varied input and output"... – JimmyB May 15 at 12:03
• The input is current and the output is voltage but I'm not sure how to calculate the time constant from that – Tsz Yee Ha May 15 at 12:26
• Vem is the O/C voltage. | R1 + R0 govern the voltage droop under load. - Vo = Vem - Iload.(R1 + R0). | The Vo/c sags after a load is removed and then restores with time to Vem - on fact this is not true as Vem will drop over time as the battery is depleted - but this model does not show that. SO If Vem drops to say Vl under load of Iload, recovers instantly to Vr1 when load is removed then recovers to Vem after time Tr then. | Vload = Vem - (R0+R1) x Iload - rearrange to get R0 + R1. | Vc = Vem-- Vr1. -> Calculate ratio of R0 to R1. | Recovery time t= R0.C. -> calculate C – Russell McMahon May 15 at 12:58

## 1 Answer

Is this an assignment or homework?

Vem is the O/C voltage.

R1 + R0 govern the voltage droop under load.
Vo = Vem - Iload.(R1 + R0).

The Vo/c sags after a load is removed and then restores with time to Vem.
In fact, the action is more complex than this as Vem will drop over time as the battery is depleted - but this model does not show that.

SO If
- Vem drops to say Vl under load of Iload,
- recovers instantly to Vr1 when load is removed
- then recovers to Vem after time Tr

then
Vload = Vem - (R0+R1) x Iload - rearrange to get R0 + R1.

Vc = Vem-- Vr1. -> Calculate ratio of R0 to R1.

Recovery time t = time constant or R0 and C. As T=RC.
Tr = R0.C -> calculate C