Explain the purpose of Thevenin's theorem in circuit analysis.

Thevenin's theorem is a powerful tool in circuit analysis that simplifies complex linear circuits into a simpler equivalent circuit consisting of a single voltage source and a single series resistance. Its primary purpose is to make it easier to analyze the behavior of a circuit when changes are made to a specific part of the circuit, particularly the load connected to it. A linear circuit is one in which the components' electrical characteristics, such as resistance, capacitance, and inductance, remain constant regardless of the voltage or current applied. Thevenin's theorem allows you to replace any complex network of resistors, voltage sources, and current sources with a single voltage source (Vth), called the Thevenin voltage, and a single series resistance (Rth), called the Thevenin resistance. The Thevenin voltage (Vth) is the open-circuit voltage at the terminals of the original circuit where the load is connected. The Thevenin resistance (Rth) is the resistance seen looking back into the circuit from those same terminals, with all voltage sources short-circuited and all current sources open-circuited. Once the Thevenin equivalent circuit is determined, you can easily calculate the current and voltage for different load resistances connected to the terminals. For instance, if you want to analyze how the voltage across a variable resistor changes as you adjust its resistance, using Thevenin's theorem simplifies the calculations significantly compared to analyzing the original complex circuit each time. Thevenin's theorem is particularly useful when analyzing circuits with multiple sources and complex interconnections, making it a valuable tool for troubleshooting and designing electronic circuits, including those found in medical devices.