Internal Resistance Calculator

Calculate the internal resistance of a battery or voltage source using the EMF, terminal voltage, and load current. Essential for understanding battery performance and power delivery.

INTERNAL RESISTANCE (r)
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Voltage Drop (I×r)
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Power Lost in r
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Load Resistance
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Efficiency
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What Is Internal Resistance?

Internal resistance is the inherent resistance within a battery, generator, or other voltage source that causes the terminal voltage to drop below the electromotive force (EMF) when current flows. Every real voltage source has some internal resistance due to the resistance of its electrodes, electrolyte, connections, and chemical reaction kinetics. This internal resistance is modeled as a small resistor in series with an ideal voltage source.

Internal resistance is a key indicator of a battery's health and performance. A new battery has low internal resistance, allowing it to deliver high currents efficiently. As a battery ages or discharges, its internal resistance increases, causing greater voltage drops under load, reduced power delivery, and more heat generation. Measuring internal resistance is one of the primary methods for assessing battery state of health (SOH).

Internal Resistance Formula

r = (ε - Vt) / I
Vt = ε - I × r    |    Plost = I² × r

Where ε is the EMF (open-circuit voltage), Vt is the terminal voltage under load, I is the load current, and r is the internal resistance. The efficiency of power delivery is the ratio of power delivered to the load versus total power generated.

Typical Internal Resistance Values

Battery TypeInternal ResistanceNotes
Car battery (12V lead-acid)5-20 mΩMust deliver 200+ A for starting
AA alkaline (1.5V)100-300 mΩIncreases as battery discharges
18650 Li-ion cell20-80 mΩLower for high-drain cells
9V battery1-2 Ω6 cells in series, each adds resistance
Coin cell (CR2032)10-30 ΩDesigned for very low currents

Effects on Performance

  • Voltage sag: Higher internal resistance causes greater voltage drop under load, reducing the usable voltage for the circuit.
  • Heat generation: Power dissipated in internal resistance (I²r) becomes heat, reducing efficiency and potentially damaging the battery.
  • Maximum current: The short-circuit current is limited to ε/r, and the maximum power transfer occurs when load resistance equals internal resistance.
  • Battery aging: Internal resistance increases over a battery's lifetime due to electrode degradation and electrolyte decomposition.

Frequently Asked Questions

How do you measure internal resistance?

The simplest method is to measure the open-circuit voltage (EMF), then connect a known load and measure the terminal voltage and current. The internal resistance is r = (EMF - Vterminal) / I. Professional battery testers use AC impedance methods at specific frequencies (typically 1 kHz) for more accurate and repeatable measurements without significantly discharging the battery.

What happens at maximum power transfer?

Maximum power is delivered to the external load when the load resistance equals the internal resistance (Rload = r). At this point, exactly half the power is dissipated internally and half is delivered to the load, giving 50% efficiency. For batteries, we usually want efficiency much higher than 50%, so we use loads with much higher resistance than the internal resistance.

Why does internal resistance increase with age?

In lithium-ion batteries, aging causes growth of the solid electrolyte interphase (SEI) layer, loss of active material, electrolyte decomposition, and electrode cracking. In lead-acid batteries, sulfation of the plates and corrosion of the grid structure increase resistance. Temperature extremes and deep discharge cycles accelerate these degradation processes.