The terminal voltage (\(V_T\)) of a battery is the electrical potential difference measured across its positive and negative terminals when connected to a circuit. This value is the actual usable voltage delivered to the external load, such as an appliance or device. It measures the energy per unit charge the battery provides to drive current through the system.
The Core Difference: Terminal Voltage vs. EMF
The terminal voltage (\(V_T\)) should not be confused with the Electromotive Force (\(\mathcal{E}\)), which is the theoretical maximum voltage a source can provide. EMF is the total potential difference created by the battery’s chemical reactions when no current is flowing, essentially the open-circuit voltage. It is the energy supplied per unit charge to drive current through the entire circuit, including the battery’s internal components.
\(V_T\), by contrast, is the actual potential difference measured only when the circuit is closed and current is drawn. During normal operation, the terminal voltage is always lower than the EMF because some energy generated within the battery is consumed internally. The EMF represents the source’s total capability, while the terminal voltage represents its delivered output.
The Role of Internal Resistance
The reason the terminal voltage is lower than the EMF is the existence of internal resistance, denoted by the letter \(r\). All power sources, including batteries, possess some internal resistance due to the materials used in their construction, such as the electrodes and the electrolyte solution. This resistance is physically located within the boundary of the battery itself.
When current (\(I\)) flows through the external circuit, it must also flow through the battery’s internal resistance. This flow causes a voltage drop inside the battery, which can be calculated using Ohm’s Law as the product of the current and the internal resistance (\(Ir\)). This voltage drop represents the electrical energy converted into heat within the battery. The internal voltage drop is precisely the amount by which the terminal voltage is reduced from the EMF.
Calculating Terminal Voltage in Discharging Circuits
When a battery is supplying power to an external load—a process known as discharging—the terminal voltage is found by subtracting the internal voltage drop from the Electromotive Force. This relationship is mathematically expressed by the formula: \(V_T = \mathcal{E} – Ir\). In this equation, \(V_T\) is the terminal voltage in Volts, \(\mathcal{E}\) is the EMF in Volts, \(I\) is the current flowing in Amperes, and \(r\) is the internal resistance in Ohms.
To determine the terminal voltage, one must first accurately find the values for the three variables on the right side of the equation. The EMF (\(\mathcal{E}\)) is typically the easiest to find, as it is the voltage measured across the battery’s terminals when the circuit is open and \(I\) is zero. The current (\(I\)) is measured by placing an ammeter in series with the external load to record the rate of charge flow.
The internal resistance (\(r\)) is a property of the battery that can be calculated by rearranging the terminal voltage formula to \(r = (\mathcal{E} – V_T) / I\). This calculation requires measuring the terminal voltage while a known current is being drawn.
For instance, a 12-Volt car battery might have an EMF of \(12.8\) Volts, but when starting a car, it might draw \(100\) Amperes, dropping the terminal voltage to \(10.5\) Volts. In this example, the internal voltage drop is \(12.8 \text{ V} – 10.5 \text{ V} = 2.3 \text{ V}\). The internal resistance would then be calculated as \(2.3 \text{ V} / 100 \text{ A} = 0.023 \text{ Ohms}\). This calculation shows that the terminal voltage is highly dependent on the current being drawn; the more current pulled from the source, the lower the actual voltage delivered to the load.
Terminal Voltage During Charging
When an external power source is used to replenish the stored energy in a battery, the battery is said to be charging. In this scenario, the current is forced to flow in the reverse direction, into the battery’s positive terminal. The terminal voltage of the battery during charging is therefore higher than its EMF.
The external source must supply enough voltage to overcome both the battery’s inherent EMF and the voltage drop caused by the current flowing through its internal resistance. This means the internal voltage drop is now added to the EMF to find the terminal voltage. The formula for the terminal voltage during charging is \(V_T = \mathcal{E} + Ir\).
The \(Ir\) term is still present because the internal resistance continues to resist the flow of current. Since the current is flowing inward, the external voltage must be elevated to push the charge through that resistance. Consequently, a charger must supply a terminal voltage that is slightly greater than the battery’s rated EMF to successfully drive the charging current.