Section 2.7 Application of Thevenin Equivalent Cicruits: Batteries
Batteries have a complicated voltage and resistance internally, as do power supplies, function generators, and other voltage sources that may be present in a circuit. All can be represented by a Thevenin equivalent circuit.
The Thevenin equivalent representation of a battery can help us understand the behavior of batteries when connected to resistive loads as pictured in Figure 2.7.1. Here, the chemical reactions inside the battery maintain an internal voltage difference \(V_\text{source}\text{.}\) There is an internal resistance \(R_\text{internal}\) that means that the actual battery terminals that we have access to provide a voltage difference of \(V_\text{battery}\ne V_\text{source}\text{.}\)
If we connect a resistive load with resistance \(R_\text{load}\text{,}\) we find that we have a voltage divider circuit where
\begin{equation*}
V_\text{battery}=\frac{R_\text{load}}{R_\text{internal} + R_\text{load}} V_\text{source}\text{.}
\end{equation*}
So, if \(R_\text{load}\) is very large \(\left(R_\text{load}\gg R_\text{internal}\right)\text{,}\) we call this a “light” resistive load because \(V_\text{battery}\approx V_\text{source}\text{.}\) Conversely, if \(R_\text{load}\) is very small \(\left(R_\text{load}\ll R_\text{internal}\right)\text{,}\) we call this a “heavy” resistive load because \(V_\text{battery}\ll V_\text{source}\text{.}\)
The analysis above shows why the voltage between battery terminals can ‘droop’ lower than their rated voltage when a heavy resistive load is connected to it. We will discuss this effect in greater detail in Section 3.9.
