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ME 140L - Prelab 4

# ME 140L - Prelab 4 - PRELAB 4 VOLTAGE DIVIDER PARALLEL RLC...

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PRELAB 4 VOLTAGE DIVIDER PARALLEL RLC CIRCUIT NATURAL RESPONSE SERIES RLC CIRCUIT STEP RESPONSE SERIES AND PARALLEL RLC CIRCUITS RESONANCE 1. OBJECTIVES square4 Learn how to build a voltage divider square4 Recognize the step response of basic series and parallel RLC circuits square4 Compute the natural frequencies of RLC circuits 2. NOTATIONS C : Capacitance (Farads) f : frequency (Hertz) I : Current (Amperes) L : Inductance (Henries) R : Resistance (Ohms) V : Voltage (Volts) τ : Time constant (Seconds) ω N : Resonant radian frequency (Radians/s) ω d : Damped frequency (Radians/s) ξ : Damping ratio. 3. VOLTAGE DIVIDER Sometimes it is important to have two different voltages when we only have available one power source at a fixed voltage. This is specially the case in electronic circuits. A voltage divider circuit allows you to obtain two different voltages. The following figure represents a voltage divider. Extracted from “Introduction to Lab EE43” www.Berkeley.edu

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Applying Kirchoff’s law on a voltage divider we get the following equation: 2 1 IR IR V X + = 1 1 IR V = 2 2 IR V = 2 1 1 1 R R R V V X + = 2 1 2 2 R R R V V X + = 4. PARALLEL RLC NATURAL RESPONSE The first step to find the step response in an electric circuit is to derive the circuit equation based both on the Kirchoff’s laws and on the elements constitutive relations. Extracted from “Circuits Laboratory” – Lamar University The figure above represents a basic parallel RLC circuit. We are interested in measuring the voltage across every element in the circuit (which happens to be the same). For the purpose of finding the natural response of the circuit, we will assume that V IN =0. Then the circuit equation is:
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