16. a. Determine the Thevénin equivalent circuit for the net- work external to the resistor R in Fig. 9.140. b. Find the current through the resistor R if its value is 20 Ω, 50 Ω, and 100 Ω. c. Without having the Thévenin equivalent circuit, what would you have to do to find the current through the resistor R for all the values of part (b)? R1 R3 R5 20 Ω 12Ω E 20 V R2 R416 N

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Thevenin Theorem

Any linear circuit, no matter how complex, maybe simplified to an equivalent circuit utilizing only a single voltage source and series resistance coupled to a load, according to Thevenin's Theorem. The superposition principle says that all foundational equations must be linear, and the notion of "linear" is still the same (i.e., there should not be any exponentials or roots). This is particularly the case when operating with passive elements like resistors, inductors, and capacitors. However, some components (particularly some gaseous and semiconductor devices like tunnel diode, Schottky diode, transistors like BJT, MOSFET) are nonlinear, meaning their current resistance fluctuates with voltage and current. As a result, circuits made up of these parts are known as nonlinear circuits.