Calculation
Uterm = Uq − Ia·Ri
Load current produces a voltage drop across internal resistance that reduces the source voltage available at the terminals.
Busch 2006, Abschnitt 4.1.4 Reale Spannungsquelle
Loaded DC source terminal voltage
Load current produces a voltage drop across internal resistance that reduces the source voltage available at the terminals.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Terminal voltage Uterm — Voltage actually available at the source terminals under the stated load.
- Open-circuit source voltage Uq — Internal unloaded voltage of the source, e.g. nominal battery voltage or cell EMF.
- Load current Ia — DC current delivered by the source to the connected load at the operating point.
- Internal resistance Ri — Equivalent source resistance including electrodes, electrolyte or winding and internal connections.
Example
Uq=12 V, Ia=5 A and Ri=0.2 Ω give a 1 V drop, Uterm=11 V and internal power loss Ia²·Ri=5 W.
Assumptions and limits
Linear source with constant Ri under steady DC load; state of charge, temperature dependence of Ri and dynamic terminal behaviour are excluded.
Understand Loaded DC source terminal voltage
This calculator models a real DC source as an ideal source voltage in series with an internal resistance, showing how far terminal voltage drops below open-circuit voltage under load.
What does this quantity describe?
From the real-source equivalent circuit, Uterm=Uq−Ia·Ri. The term Ia·Ri is the internal voltage drop; it grows proportionally with drawn current and reduces the voltage available to the load.
Formula and variables
Uterm = Uq − Ia·Ri
Uterm = Uq − Ia·RiPv = Ia²·RiRi = (Uq−Uterm)/Ia
| Symbol / input | Meaning |
|---|---|
| Terminal voltage Uterm | Voltage actually available at the source terminals under the stated load. |
| Open-circuit source voltage Uq | Internal unloaded voltage of the source, e.g. nominal battery voltage or cell EMF. |
| Load current Ia | DC current delivered by the source to the connected load at the operating point. |
| Internal resistance Ri | Equivalent source resistance including electrodes, electrolyte or winding and internal connections. |
Choose the inputs correctly
Uq is the unloaded source voltage, such as a battery's rest voltage or a supply's open-circuit voltage. Ia is the actually drawn DC current. Ri is the source's internal equivalent resistance at this operating point.
How to use the calculator
Measure Uq unloaded where possible, then record Ia and the corresponding terminal voltage under load; Ri can be back-calculated as (Uq−Uterm)/Ia or taken from a datasheet.
Worked example
Uq=12 V, Ia=5 A and Ri=0.2 Ω give a 1 V drop, so Uterm=11 V, and internal power loss Ia²·Ri=5 W.
Understand the result and units
A large gap between Uterm and Uq indicates high internal resistance or heavy load. At short circuit (Uterm=0) the model gives the theoretical short-circuit current Uq/Ri.
Uq and Uterm are voltages, Ia a current and Ri a resistance. All values are converted internally to coherent SI units.
Typical applications
Estimating voltage sag of batteries, rechargeable cells, solar cells or simple power supplies under load, and a basis for sizing buffer capacitors or cable cross-sections.
Assumptions, limits and common mistakes
Linear source model with constant Ri under steady DC load. State-of-charge dependence, temperature effects on Ri, AC components and dynamic settling behaviour are excluded.
Common mistake: Do not accidentally enter the loaded terminal voltage as Uq. Do not confuse Ri with the load resistance; both sit in the same circuit but are distinct quantities.
Frequently asked questions
What is “Loaded DC source terminal voltage” used for?
Estimating voltage sag of batteries, rechargeable cells, solar cells or simple power supplies under load, and a basis for sizing buffer capacitors or cable cross-sections.
Where do the input values come from?
Uq is the unloaded source voltage, such as a battery's rest voltage or a supply's open-circuit voltage. Ia is the actually drawn DC current. Ri is the source's internal equivalent resistance at this operating point.
What does the result not cover?
Linear source model with constant Ri under steady DC load. State-of-charge dependence, temperature effects on Ri, AC components and dynamic settling behaviour are excluded.