Internal resistance (\(r\)) is an inherent property of all real-world electrical power sources, such as batteries and generators. It represents the opposition to the flow of electric current that exists within the source itself, acting like internal electrical friction. This resistance is unavoidable because a battery is a complex chemical system, not a perfect conductor, and it causes energy to be lost as heat inside the source.
The Physical Origin of Internal Resistance
Internal resistance is not a single, fixed resistor but a combination of physical and electrochemical hindrances to charge movement inside the cell. One major component is ohmic resistance, which includes the physical electrical resistance of the cell’s materials. This incorporates the conductivity of the metallic current collectors, the electrodes, and the contact resistance at the interfaces between different components.
A significant portion of internal resistance comes from the electrolyte, the substance through which ions move to complete the circuit. This ionic resistance arises because the movement of ions is slower and more constrained than the flow of electrons through a wire. Factors like electrolyte concentration, type, and the distance between electrodes influence this resistance.
The chemical reactions also introduce resistance, known as charge transfer or polarization resistance, as ions cross the interface between the liquid electrolyte and the solid electrode. As a battery ages, irreversible side-reactions can create insulating layers on the electrodes, increasing resistance and decreasing power delivery. Low temperatures also temporarily increase internal resistance by reducing the mobility of ions in the electrolyte.
The Relationship Between Internal Resistance and Terminal Voltage
The existence of internal resistance causes the voltage to drop when current is drawn from the battery. The maximum theoretical voltage a battery can supply is the Electromotive Force (\(\mathcal{E}\) or EMF), measured when no current is flowing (open circuit). When current (\(I\)) flows, the internal resistance (\(r\)) resists this flow, consuming some of the energy generated by the chemical reactions.
This energy consumption manifests as a voltage drop across the internal resistance, calculated as \(V_{drop} = I \times r\). The actual voltage available to the external circuit, the terminal voltage (\(V_T\)), is always less than the ideal EMF. This relationship is expressed as \(V_T = \mathcal{E} – Ir\), showing that the terminal voltage decreases linearly as the current drawn increases.
A higher internal resistance results in a larger \(Ir\) voltage drop, leading to a lower terminal voltage and reduced device performance. This lost voltage represents power dissipated as heat within the battery, calculated by \(P_{loss} = I^2r\). This heat generation is a sign of inefficiency, as the battery converts stored chemical energy into thermal energy instead of usable electrical power.
Determining Internal Resistance
Quantifying a battery’s internal resistance is fundamental to assessing its state of health and performance. The most straightforward conceptual method is the DC load test, which relies on measuring the voltage drop caused by a known load. The process begins by measuring the open-circuit voltage (\(\mathcal{E}\)), which is the voltage across the terminals when no current is flowing. Next, a known load is connected, current (\(I\)) flows, and the terminal voltage (\(V_T\)) is measured. The difference between \(\mathcal{E}\) and \(V_T\) is the voltage lost across the internal resistance, which, when divided by the measured current, yields the internal resistance value: \(r = (\mathcal{E} – V_T) / I\).
For quick, non-destructive testing, specialized tools often use AC impedance testing, especially in manufacturing and battery management systems. This method applies a small alternating current signal, often at a frequency of 1000 hertz, and measures the resulting voltage response. While AC impedance provides a rapid snapshot and is useful for comparison, it may yield a different value than the DC load test because it measures a complex electrical property that includes both resistance and reactance.