Internal Resistance
Calculate internal resistance of a battery using r = ε/I − R. Free physics calculator finds terminal voltage, power loss, and load dissipation with interactive charts and step-by-step breakdowns.
About This Calculator
The Internal Resistance Calculator helps students, engineers, and hobbyists determine the internal resistance of a battery or any voltage source. Internal resistance is the opposition to current flow within the source itself, caused by the electrolytes, electrodes, and internal connections. It is a key parameter that affects battery performance, efficiency, and heat generation.
The calculator uses the standard internal resistance formula: r = ε/I − R, where ε is the electromotive force (EMF) in volts, I is the current through the circuit in amperes, and R is the load resistance in ohms. From these inputs, it also computes the terminal voltage V = ε − Ir, the power dissipated in the load P_load = I²R, and the power dissipated internally as heat P_internal = I²r.
How to Use
Enter the battery's EMF (open-circuit voltage), the load resistance connected across it, and the current flowing through the circuit. Click Calculate to get the internal resistance, terminal voltage under load, and power breakdown with an interactive chart.
Applications
This calculator is useful for battery testing, power supply design, physics and engineering coursework, electric vehicle battery analysis, and troubleshooting electronics where voltage sag under load is a concern. Understanding internal resistance helps predict battery runtime, heat generation, and maximum power delivery.
Frequently Asked Questions
What is internal resistance of a battery?
Internal resistance is the opposition to current flow within a voltage source such as a battery or cell. It is caused by the resistance of electrolytes and electrodes inside the source. A new battery has low internal resistance, which increases as the battery ages.
How do you calculate internal resistance?
Internal resistance r is calculated using the formula r = ε/I − R, where ε is the electromotive force (EMF) of the source in volts, I is the current through the circuit in amperes, and R is the load resistance in ohms connected across the source.
What is terminal voltage?
Terminal voltage is the voltage output measured across the terminals of a battery or voltage source when a load is connected. It is calculated as V = ε − Ir, where ε is the EMF, I is the current, and r is the internal resistance. Terminal voltage is always less than the EMF when current flows.
What is the internal resistance of an ideal voltage source?
An ideal voltage source has zero internal resistance. This means it can maintain a constant output voltage regardless of the current drawn. Real batteries always have some non-zero internal resistance, which causes the terminal voltage to drop under load.
Why does internal resistance matter in circuit design?
Internal resistance limits the maximum current a battery can deliver and causes power loss as heat inside the battery. High internal resistance reduces efficiency, causes voltage sag under load, and generates heat. Engineers consider it when designing power supplies, battery packs, and portable electronics.
How does internal resistance affect battery performance?
As internal resistance increases, the battery's terminal voltage drops more under load, reducing the power available to the device. The battery also heats up more due to I²r power dissipation. This is why old or damaged batteries may show a good open-circuit voltage but fail under load.
Can I measure internal resistance with a multimeter?
Internal resistance cannot be measured directly with a standard multimeter. It must be calculated by measuring the open-circuit voltage (EMF) and the voltage under a known load, then applying the formula r = (ε − V) / I. This calculator does the math for you instantly.