A battery functions as an electrochemical energy source, converting stored chemical energy into electrical energy. This stored energy creates an electromotive force (EMF), which represents the maximum potential difference the battery can provide. Within the battery’s structure, the materials, including the electrolyte and electrodes, naturally oppose the movement of charge. This inherent opposition is quantified as internal resistance, denoted by the symbol \(r\). This property limits the actual current that can be drawn from the power source.
Understanding the Impact of Internal Resistance
The presence of internal resistance directly influences a battery’s real-world performance. When a circuit draws current from the battery, some of the electromotive force is used to push the charge through this internal opposition. This results in a phenomenon known as voltage drop, where the terminal voltage available to the external circuit is always less than the battery’s true EMF.
This effect becomes more pronounced as the current drawn from the battery increases. A battery with a high internal resistance cannot efficiently deliver large amounts of power, even if its chemical state of charge is high. For instance, a worn-out car battery might have sufficient chemical charge, but its high internal resistance prevents it from supplying the burst of current needed to start the engine.
The energy lost overcoming internal resistance is converted into heat within the battery structure itself. This thermal generation measures inefficiency, as the energy is wasted instead of powering the external load. Excessive heat can accelerate battery degradation and potentially lead to thermal runaway. Understanding the value of \(r\) provides a measure of a battery’s health and its ability to sustain a load.
Preparing for Measurement
Before calculating the internal resistance, specific measurements must be taken under controlled conditions. The required tools for this process include a precision multimeter, which can function as both a voltmeter and an ammeter, along with a known external load. This load is typically a power resistor or a device that will draw a stable, measurable current from the battery.
The first step is determining the battery’s open-circuit voltage (\(V_{OC}\)). This is achieved by connecting the multimeter’s voltage probes directly across the battery terminals while ensuring no external load is connected. The \(V_{OC}\) measurement provides the closest practical value to the battery’s theoretical EMF, reflecting its maximum potential energy.
Once \(V_{OC}\) is recorded, the second phase involves connecting the known external load to the battery terminals. Select a load that will draw an appropriate current for the battery’s rating to avoid damage or excessive voltage drop. Safety precautions should be followed when working with electrical currents and loads.
With the load connected and current flowing, two simultaneous measurements must be taken. The ammeter is placed in series with the load to measure the current (\(I\)). Simultaneously, the voltmeter probes are placed across the battery terminals to measure the terminal voltage (\(V_T\)) while the battery is under load. These three values—\(V_{OC}\), \(V_T\), and \(I\)—form the basis for the calculation.
Calculating Internal Resistance Using Terminal Voltage
The calculation of internal resistance translates the observed electrical behavior into a quantifiable value using a foundational relationship from circuit theory. This relationship is based on the principle that the terminal voltage (\(V_T\)) available to the external circuit is the battery’s EMF (\(V_{OC}\)) minus the voltage lost internally. This internal voltage loss is precisely the product of the measured current (\(I\)) and the battery’s internal resistance (\(r\)).
This relationship is expressed mathematically by the equation \(V_T = V_{OC} – I r\). The term \(I r\) represents the voltage drop that occurs across the internal resistance when current flows. This equation directly links the battery’s internal property (\(r\)) to its external performance (\(V_T\) and \(I\)).
To isolate the internal resistance (\(r\)), the equation must be algebraically rearranged. By moving the \(I r\) term to one side and \(V_T\) to the other, the formula becomes \(I r = V_{OC} – V_T\). This difference, \(V_{OC} – V_T\), is the exact measure of the voltage lost to the battery’s internal components.
The final step in isolating the internal resistance involves dividing the voltage difference by the measured current (\(I\)). The derived formula for calculation is \(r = (V_{OC} – V_T) / I\). This formula demonstrates that the internal resistance is simply the ratio of the lost voltage to the current that caused the loss.
To illustrate this process, consider a practical example using typical measurements. Suppose a battery is measured to have an open-circuit voltage (\(V_{OC}\)) of \(1.50\) Volts. When an external load is connected, the current (\(I\)) flowing through the circuit is measured to be \(0.50\) Amperes, and the terminal voltage (\(V_T\)) drops to \(1.30\) Volts.
The first step in the calculation is determining the voltage lost internally: \(V_{OC} – V_T\). Using the example values, \(1.50\) Volts minus \(1.30\) Volts equals \(0.20\) Volts. This \(0.20\) Volts represents the energy dissipated within the battery.
The final step involves applying the derived formula: \(r = (0.20 \text{ V}) / (0.50 \text{ A})\). Performing the division yields a result of \(0.40\) Ohms (\(\Omega\)). Therefore, the calculated internal resistance for this battery is \(0.40 \Omega\).
This method provides a direct and practical way to assess a battery’s condition without needing to dismantle the device. A low value of \(r\) indicates a healthy battery that can efficiently deliver current, while an increasing value often signals chemical degradation or depletion. Regular measurement of \(r\) offers a more accurate assessment of a battery’s capacity to deliver power than simply checking its open-circuit voltage.