Our internal resistance calculator allows you to calculate the resistance offered by a voltage source to the flow of current through it. Do you know that both trucks and motorcycles use batteries of identical electromotive force (emf = 12 V)? However, the truck battery can deliver a much larger charge than the motorcycle one due to its smaller internal resistance.
To know more about internal resistance, continue reading. You will learn:
- What is internal resistance?
- How to find the internal resistance of a battery.
- What is the internal resistance of an ideal voltage/current source?
If you want to calculate the resistance of a conductor instead, head on to a wire resistance calculator.
What Is Internal Resistance — Internal Resistance Definition
The internal resistance of a voltage source (e.g., a battery) is the resistance offered by the electrolytes and electrodes of the battery to the flow of current through the source. It is usually denoted by the symbol r.
The internal resistance of a new battery is usually low; however, as the battery is put to more and more use, its internal resistance increases. This is one of the main reasons an old battery struggles to deliver enough current.
How to Find the Internal Resistance of a Battery — Internal Resistance Formula
Let us consider a cell of electromotive force (emf) ε and internal resistance r. If we connect this cell to an external load resistor R, the total resistance RT of the circuit becomes:
According to Ohm's law, the current I through the circuit is:
The voltage measured across the battery terminals while it is under load — the terminal voltage V — is lower than the emf, because some voltage drops across the internal resistance:
This last equation is the internal resistance formula used by the calculator: measure the emf (open-circuit voltage), the terminal voltage under load, and the current, and the internal resistance follows.
Calculating Internal Resistance — An Example
A battery has an emf of ε = 12 V. When connected to a load it supplies a current of I = 2.8 A, and the terminal voltage measured across it drops to V = 11.2 V. Find the internal resistance.
r = (ε − V) / I = (12 − 11.2) / 2.8 = 0.286 Ω
R = V / I = 11.2 / 2.8 = 4 Ω (load resistance)
RT = ε / I = 12 / 2.8 = 4.286 Ω = r + R
η = V / ε × 100% = 11.2 / 12 × 100% = 93.3% (efficiency)
How to Use the Internal Resistance Calculator
- Enter the electromotive force (emf, ε) of the source — its open-circuit voltage (mV, V, or kV).
- Enter the terminal voltage (V) measured across the source while it is delivering current.
- Enter the current (I) flowing through the circuit (mA, A, or kA).
- Pick a power unit system — Metric (mW, W, kW) or American (HP, BTU/hr).
- The calculator returns the internal resistance, load resistance, total resistance, the power distribution, and the efficiency.
Unit Systems
Electrical quantities — volts (V), amperes (A), and ohms (Ω) — are SI units shared by both the metric and the American systems, so the inputs use the standard SI prefixes (mV/V/kV, mA/A/kA). The power unit system option controls how the total generated power is reported:
- Metric (SI): mW, W, kW
- American: HP (1 HP = 745.7 W), BTU/hr (1 W ≈ 3.412 BTU/hr)
FAQs
What is the internal resistance of an ideal voltage source?
An ideal voltage source has zero internal resistance, so its terminal voltage equals its emf no matter how much current it delivers. Real sources always have some internal resistance.
What is the internal resistance of an ideal current source?
An ideal current source has infinite internal resistance, which lets it push the same current regardless of the load connected to it.
Why does a battery's terminal voltage drop under load?
When current flows, a voltage equal to I·r is dropped across the internal resistance, so the voltage available at the terminals is V = ε − I·r — lower than the emf. The larger the current or the internal resistance, the bigger the drop.
Why can a truck battery deliver more current than a motorcycle battery?
Even though both may have the same emf (12 V), the truck battery has a much smaller internal resistance. A smaller r means a smaller voltage drop inside the battery, so it can supply a much larger current to crank a bigger engine.
Does internal resistance change over time?
Yes. The internal resistance of a battery generally increases as it ages and is discharged, which reduces the current it can deliver and lowers its efficiency.