Now, you will use what you have learned so far to solve a large system of equations. Consider the circuit below: V1 19 V2 1 A 252 ww V3 252 www 252 V4 Then, you need to solve the system as indicated above. www www V5 To solve this problem, you will need to use the node-voltage method to set up the system of linear equations in terms of the node-voltages U1, U2, U3, U4, and U5, and write them in the matrix equation form: AU = b.

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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.