Internal Resistance Calculator
Free calculate battery internal resistance from emf, terminal voltage, and current using r = (emf - v)/i.
Input Parameters
Voltage when no current flows
Voltage when current is flowing
Results
Enter values to calculate
What is Internal Resistance?
Internal resistance is the resistance within a battery or power source that causes voltage drop when current flows. It's modeled as a resistor in series with an ideal voltage source (EMF).
When a battery supplies current, the terminal voltage drops below the EMF due to internal resistance. This voltage drop increases with current, following V = EMF - I×r, where r is the internal resistance.
Internal resistance affects battery performance, efficiency, and voltage regulation. Lower internal resistance means better performance, especially under high current loads. It increases as batteries age or discharge.
Internal Resistance Formula
Where:
- • r = Internal resistance (Ω)
- • EMF = Electromotive force / Open-circuit voltage (V)
- • V = Terminal voltage under load (V)
- • I = Current (A)
Terminal voltage: V = EMF - I×r
How to Calculate Internal Resistance
-
1
Measure EMF (open-circuit voltage)
Measure battery voltage with no load connected. This is the EMF.
-
2
Measure terminal voltage under load
Connect a load and measure the voltage while current flows.
-
3
Measure current
Measure the current flowing through the circuit.
-
4
Calculate internal resistance
r = (EMF - V) / I
Practical Examples
Example 1: Car Battery
A car battery has EMF of 12.5 V. When delivering 50 A, terminal voltage is 12.0 V. Calculate internal resistance.
Solution:
r = (EMF - V) / I = (12.5 V - 12.0 V) / 50 A
r = 0.5 V / 50 A = 0.01 Ω = 10 mΩ
Example 2: AA Battery
An AA battery has EMF of 1.5 V. Under 0.5 A load, voltage drops to 1.4 V. What is internal resistance?
Solution:
r = (1.5 V - 1.4 V) / 0.5 A
r = 0.1 V / 0.5 A = 0.2 Ω
Applications
Battery Testing
Evaluating battery health, capacity, and performance. Higher internal resistance indicates aging or degradation.
Power Supply Design
Understanding voltage regulation, load regulation, and designing power systems with appropriate source impedance.
Electronics
Designing circuits that account for source resistance, voltage drop, and power delivery limitations.
Battery Management
Monitoring battery state, determining when to replace batteries, and optimizing charging strategies.
Frequently Asked Questions
Why does terminal voltage drop under load?
Internal resistance causes a voltage drop (I×r) when current flows. Terminal voltage = EMF - I×r, so higher current means lower terminal voltage.
What is a typical internal resistance value?
Car batteries: 0.01-0.05 Ω, AA batteries: 0.1-0.5 Ω, lithium-ion: 0.01-0.1 Ω. Lower is better for high-current applications.
Does internal resistance change?
Yes! Internal resistance increases as batteries age, discharge, or operate at extreme temperatures. It's a key indicator of battery health.
What is the Thevenin equivalent?
A battery can be modeled as an ideal voltage source (EMF) in series with internal resistance. This is the Thevenin equivalent circuit.
How does internal resistance affect power delivery?
Power lost internally = I²r. Higher internal resistance means more power wasted as heat inside the battery, reducing efficiency and available power.