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</center><p>In the limit R →0 the RLC circuit reduces to the lossless LC circuit shown on FigureS C L vc +-+ vLFigureThe equation that describes the response of this circuit isdvc vc dt LC + = () Assuming a solution of the form Aest the characteristic equation is s +ωο = () Whereο LC ω= The two roots are Typically the  Discuss the purpose and behavior of RLC circuitsCalculate the resonant frequency of an RLC circuitMeasure and confirm the resonant frequency using Band-stop filters are used in applications such as reducing audio feedback in instrument amplifiers. These two cases are shown in figurebelow. V R = i R; V L = L di dt; V C =C Z i dt: * A parallel RLC circuit driven by a constant voltage source is trivial to analyze Îcosφ is the “power factor”. For example, RLC circuits are used for voltage magnification and parallel RLC circuits can be used for current magnification. L-R-C in Series We will start by treating the case of an L-R-C circuit in series: C − + v C i C + − vL iL R L StepDeriving the Differential Equation From the constitutive relations for a capacitor and an inductor, we can write iC = C dvC dt, and vL = L diL dt. We will analyze this circuit in order to determine its transient characteristics once the switch S is closed Application: RLC Electrical Circuits. RLC circuits have countless applications outside of being filters. Circuit. Since the current through each element is known, the voltage can be found in a straightforward manner. What do the response curves of over-, under-, and critically-damped circuits look like? (1) We can then use KVL around the L-R-C loop to derive the equa The LC circuit. Key points. Another use for RLC circuits is in induction heating * A series RLC circuit driven by a constant current source is trivial to analyze. How to choose R, L, C values to achieve fast switching or to prevent Missing: applications The circuit shown on Figureis called the series RLC circuit. X L − X C. To maximize power delivered to circuit ⇒ make φ close to zero Max power delivered to load happens at resonance. E.g., too much inductive reactance (X L) can be cancelled by increasing X (e.g., circuits with large motors) C circuit. In Section F, we explored first-order differential equations for electrical circuits consisting of a voltage source with either a resistor and  The typical LRC circuit consists of a resistor, capacitor, and induc-tor either in parallel or in a series loop configuration.</p></translate>
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