+ VL ell Vị Problem 2: Appearing to the right is again our famil- iar RLC series circuit, this time with a new voltage la- bel, v1. Also once again, for your solving convenience, is a solution for this circuit when the voltage source is + constant. Va C i1-part (t) = 0 R SKie4it + K2eª2t, (Kjeait + K2teªit, if a1 = a2. if a1 7 a2; i1-cor 1-comp(t) i1(t) = i1-comp(t)+i1-part (t) where R + 2L' V(2L R R a2 = – 1 R 1 a1 = – and LC 2L V(2L LC Find an expression for v1(t) assuming a1 # a2. There is no need to solve for K1 and K2 in this problem. Hint: Those of you who are still unsure of the difference between a voltage drop and a voltage with respect to ground: learn it now! In terms of R, L, C, va, K1, K2, a1, and a2 # a1 the voltage v1(t) + I

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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.