Internal Resistance Calculator

Calculate the internal resistance of batteries, power sources, and electrical components.

Determine the internal resistance of electrical sources by measuring voltage drops under load. Essential for understanding power source efficiency and performance.

Examples

Click on any example to load it into the calculator.

Automotive Battery

Automotive Battery

Typical car battery under moderate load conditions.

Open Circuit Voltage: 12.6 V

Load Resistance: 5 Ω

Loaded Voltage: 12.2 V

AA Alkaline Battery

AA Alkaline Battery

Fresh AA battery under typical load for portable electronics.

Open Circuit Voltage: 1.58 V

Load Resistance: 10 Ω

Loaded Voltage: 1.52 V

Industrial Power Supply

Industrial Power Supply

High-current power supply for industrial applications.

Open Circuit Voltage: 24.0 V

Load Resistance: 2 Ω

Loaded Voltage: 23.5 V

Current: 11.75 A

Solar Panel

Solar Panel

Solar panel under standard test conditions.

Open Circuit Voltage: 18.5 V

Load Resistance: 15 Ω

Loaded Voltage: 17.8 V

Other Titles
Understanding Internal Resistance: A Comprehensive Guide
Master the concept of internal resistance and learn how it affects the performance of batteries, power supplies, and electrical systems. This guide covers everything from basic principles to advanced applications.

What is Internal Resistance?

  • Basic Definition
  • Physical Origins
  • Impact on Performance
Internal resistance is the inherent resistance within a power source that opposes the flow of current. It's a fundamental property of all electrical sources, including batteries, generators, and power supplies. This resistance causes a voltage drop when current flows, reducing the effective voltage available to the load. Understanding internal resistance is crucial for designing efficient electrical systems and predicting power source performance under various load conditions.
Physical Origins of Internal Resistance
Internal resistance arises from several physical factors within the power source. In batteries, it includes the resistance of electrolyte, electrode materials, and internal connections. In generators, it includes winding resistance and magnetic losses. Even the best power sources have some internal resistance - it's impossible to eliminate completely. The goal is to minimize it for maximum efficiency and power delivery.
Why Internal Resistance Matters
Internal resistance directly affects how much power a source can deliver to a load. A high internal resistance means more voltage is lost internally, leaving less for the external circuit. This becomes critical in applications requiring high current, such as automotive starters, power tools, or high-performance electronics. Understanding internal resistance helps engineers design better systems and users choose appropriate power sources for their needs.
The Voltage Drop Phenomenon
When you connect a load to a power source, the voltage at the terminals drops from the open-circuit voltage. This drop is proportional to the current and the internal resistance. The relationship is described by the equation: V = V₀ - Ir, where V is the terminal voltage, V₀ is the open-circuit voltage, I is the current, and r is the internal resistance. This simple equation is the foundation of internal resistance calculations.

Typical Internal Resistance Values:

  • AA Alkaline Battery: 0.1-0.3 Ω (fresh), 0.5-1.0 Ω (depleted)
  • Car Battery: 0.01-0.05 Ω (good condition), 0.1-0.3 Ω (weak)
  • Lithium-ion Battery: 0.05-0.2 Ω (varies with chemistry and capacity)
  • Power Supply: 0.001-0.01 Ω (high-quality units)
  • Solar Panel: 0.1-1.0 Ω (depends on size and technology)

Step-by-Step Guide to Using the Calculator

  • Measurement Setup
  • Data Collection
  • Calculation Process
Using the internal resistance calculator requires accurate measurements and understanding of the underlying physics. Follow these steps carefully to obtain reliable results.
1. Prepare Your Measurement Setup
You'll need a voltmeter (preferably digital for accuracy), a known load resistance, and the power source to be tested. The load resistance should be appropriate for the power source - too small and you might damage the source, too large and the voltage drop will be too small to measure accurately. For most batteries, a load resistance of 1-10 times the expected internal resistance works well.
2. Measure Open Circuit Voltage
First, measure the voltage across the power source terminals with no load connected. This is your V₀ value. Ensure the source is in a stable state - for batteries, let them rest for a few minutes after any previous use. Record this value accurately, as it's the baseline for all calculations.
3. Connect Load and Measure Loaded Voltage
Connect your known load resistance across the terminals and measure the voltage again. This is your V value. The voltage should drop from the open-circuit value. If it doesn't drop significantly, your load resistance might be too large. If it drops too much, your load might be too small and could damage the source.
4. Calculate or Measure Current
You can either measure the current directly with an ammeter in series with the load, or calculate it using Ohm's Law: I = V/R. The calculator can work with either approach. Direct measurement is more accurate but requires additional equipment.
5. Input Values and Interpret Results
Enter your measured values into the calculator. The tool will calculate the internal resistance and provide additional useful metrics like short-circuit current and maximum power transfer capability. These results help you understand the power source's capabilities and limitations.

Measurement Tips:

  • Use a digital multimeter with at least 3.5 digits for voltage measurements
  • Ensure good electrical connections to minimize contact resistance
  • Allow the power source to stabilize before measurements
  • Take multiple readings and average them for better accuracy
  • Consider temperature effects - internal resistance varies with temperature

Real-World Applications and Practical Uses

  • Battery Testing
  • Power Supply Design
  • Troubleshooting
Internal resistance calculations have numerous practical applications across various industries and everyday situations.
Battery Health Assessment
Internal resistance is one of the best indicators of battery health. As batteries age, their internal resistance increases, reducing their ability to deliver current. By monitoring internal resistance over time, you can predict when a battery needs replacement before it fails completely. This is especially important in critical applications like medical devices, backup power systems, and automotive applications.
Power Supply Design and Selection
When designing electronic circuits, understanding the internal resistance of power sources helps engineers choose appropriate components and design efficient power distribution systems. High internal resistance can cause voltage regulation problems and limit the maximum current available to the load. This knowledge is crucial for designing reliable electronic systems.
Automotive and Marine Applications
In automotive and marine applications, internal resistance testing is essential for battery maintenance. A battery with high internal resistance may show normal voltage when not loaded but fail to start the engine when high current is required. Regular internal resistance testing can prevent unexpected failures and extend battery life through proper maintenance.
Renewable Energy Systems
Solar panels and wind turbines have internal resistance that affects their power output under different load conditions. Understanding this resistance helps optimize the system design and choose appropriate inverters and charge controllers. It also helps predict system performance under various weather conditions.

Industry Applications:

  • Telecommunications: Backup battery monitoring in cell towers
  • Medical: Critical care equipment power supply reliability
  • Aerospace: Aircraft battery health monitoring
  • Industrial: UPS system maintenance and replacement planning
  • Consumer Electronics: Smartphone and laptop battery health assessment

Common Misconceptions and Technical Considerations

  • Voltage vs. Power
  • Temperature Effects
  • Measurement Accuracy
Several misconceptions surround internal resistance and its measurement. Understanding these helps avoid common pitfalls and obtain more accurate results.
Misconception: Lower Internal Resistance Always Means Better Performance
While lower internal resistance generally means better performance, it's not always the most important factor. For low-current applications, internal resistance might be negligible compared to other factors like capacity, shelf life, or cost. The optimal internal resistance depends on the specific application and load requirements.
Temperature Effects on Internal Resistance
Internal resistance varies significantly with temperature. Most batteries have higher internal resistance at low temperatures, which is why they perform poorly in cold weather. This effect is particularly important in automotive and outdoor applications. Always consider the operating temperature when interpreting internal resistance measurements.
Frequency Dependence
For AC power sources, internal resistance may vary with frequency due to inductive and capacitive effects. This is important when testing transformers, generators, or other AC power sources. The calculator assumes DC conditions, so results for AC sources should be interpreted accordingly.
Measurement Accuracy and Precision
Accurate internal resistance measurement requires precise voltage and current measurements. Small errors in voltage measurement can lead to large errors in calculated internal resistance, especially when the voltage drop is small. Using high-quality measurement equipment and taking multiple readings improves accuracy.

Technical Considerations:

  • Contact resistance can add to measured internal resistance
  • Battery internal resistance varies with state of charge
  • Some power sources have non-linear internal resistance
  • AC vs. DC internal resistance can differ significantly
  • Aging effects can change internal resistance over time

Mathematical Derivation and Advanced Concepts

  • Ohm's Law Application
  • Maximum Power Transfer
  • Efficiency Calculations
The mathematical foundation of internal resistance calculations is based on fundamental electrical principles and provides insights into power source behavior.
Derivation of the Internal Resistance Formula
The internal resistance formula r = (V₀ - V) / I is derived from applying Kirchhoff's voltage law to a simple circuit with a power source and load. The voltage drop across the internal resistance equals the difference between open-circuit and loaded voltage. This relationship is fundamental to understanding power source behavior under load.
Maximum Power Transfer Theorem
The maximum power transfer theorem states that maximum power is transferred to the load when the load resistance equals the internal resistance of the source. This is a crucial concept for designing efficient power systems. The calculator shows the maximum power transfer capability, which is P_max = V₀² / (4r).
Efficiency Considerations
Efficiency in power transfer is defined as the ratio of power delivered to the load to the total power generated by the source. It's given by η = R / (R + r), where R is the load resistance and r is the internal resistance. Higher efficiency requires load resistance much larger than internal resistance.
Short Circuit Current
Short circuit current is the maximum current a power source can theoretically deliver when its terminals are shorted together (zero load resistance). It's calculated as I_sc = V₀ / r. This value is important for safety considerations and circuit protection design.

Advanced Applications:

  • Battery modeling for electric vehicle design
  • Power system stability analysis
  • Electrochemical impedance spectroscopy
  • Solar panel maximum power point tracking
  • Uninterruptible power supply (UPS) design