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
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
Alkaline AA
0.1 - 0.3 Ω (new)
Increases with age/discharge
Li-ion 18650
0.02 - 0.1 Ω
Low internal resistance
Car Battery
0.01 - 0.02 Ω
Very low for high current
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.