Internal Resistance Calculator

Calculate internal resistance, EMF, current, and terminal voltage in electrical circuits

Calculate Internal Resistance Parameters

The ideal voltage of the battery or voltage source

External resistance connected to the voltage source

Current flowing through the circuit

Calculation Results

0.000 Ω
Internal Resistance
0.000 V
EMF
0.000 mA
Current
0.000 V
Terminal Voltage
0.000000 W
Power Dissipated (Internal)
0.0%
Efficiency

Formulas used: r = ε/I - R, V = ε - I×r, P = I²×r

Circuit parameters: Total resistance = 0.000 Ω

Voltage drop: Internal = 0.000 V, Load = 0.000 V

Circuit Analysis

Example Calculation

Battery Internal Resistance Example

Given: Battery EMF = 3.0 V, Load resistance = 995 Ω

Measured: Circuit current = 3.0 mA

Goal: Find the internal resistance of the battery

Solution

Using: r = ε/I - R

r = 3.0 V / 0.003 A - 995 Ω

r = 1000 Ω - 995 Ω

r = 5.0 Ω

Terminal voltage: V = 3.0 V - (0.003 A × 5.0 Ω) = 2.985 V

Efficiency: η = 2.985 V / 3.0 V = 99.5%

Typical Internal Resistance

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Alkaline AA

0.1 - 0.3 Ω (new)

Increases with age/discharge

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Li-ion 18650

0.02 - 0.1 Ω

Low internal resistance

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Car Battery

0.01 - 0.02 Ω

Very low for high current

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9V Alkaline

1 - 3 Ω

Higher due to small size

Key Concepts

Lower internal resistance = higher efficiency

Terminal voltage decreases with load current

Internal resistance increases with battery age

Maximum power transfer when R = r

Ideal voltage source has zero internal resistance

Understanding Internal Resistance

What is Internal Resistance?

Internal resistance is the resistance offered by the electrolytes and electrodes of a battery or voltage source to the flow of current through it. It represents the inherent opposition to current flow within the source itself.

Why is it Important?

  • Affects the actual voltage available to the load
  • Determines power transfer efficiency
  • Influences battery life and performance
  • Critical for circuit design and analysis

Key Equations

Internal Resistance: r = ε/I - R

Terminal Voltage: V = ε - I×r

Current: I = ε/(R + r)

Applications

  • Battery Testing: Assess battery health and capacity
  • Circuit Design: Optimize power transfer and efficiency
  • Power Systems: Analyze voltage regulation
  • Electronics: Design stable power supplies

Note: As batteries age or discharge, their internal resistance typically increases, reducing their ability to deliver power effectively.