Internal Resistance Calculator

Internal Resistance of a Power Source

Real batteries and power supplies have internal resistance. Terminal voltage drops when load current increases. Given EMF, terminal voltage, and current, you can find internal resistance and the power wasted inside the source.

Formulas

$$r = \frac{\text{EMF} - V_{\text{terminal}}}{I}$$ $$P_r = I^2 r$$

EMF is the open-circuit voltage, $V_{\text{terminal}}$ is the voltage under load, $I$ is load current, $r$ is internal resistance, and $P_r$ is power dissipated inside the source.

Practical Notes

A fresh alkaline cell may show low internal resistance, while a depleted one rises sharply. High discharge current increases voltage drop across $r$, reducing useful output and heating the cell.

Frequently Asked Questions

What is EMF?

Electromotive force is the potential difference with no load current. It is the theoretical maximum voltage the source can deliver.

Why is terminal voltage lower than EMF?

Load current flows through internal resistance, creating a voltage drop inside the source: V_terminal = EMF − Ir.

What does power loss in r mean?

It is energy converted to heat inside the battery or supply. Higher current and higher internal resistance both increase wasted power.

Can internal resistance be negative?

Not for a passive source. If terminal voltage exceeds EMF under your measurements, check polarity, meter range, or whether an external supply is active.

How do I measure EMF?

Measure open-circuit voltage with a high-impedance voltmeter and no load connected. Under load, use the values at a known current to calculate r.

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Internal Resistance of a Power Source

Formulas

Practical Notes

Frequently Asked Questions

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