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lab 2 - Experiment 2 Oscillation and Damping in the LRC...

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Experiment 2: Oscillation and Damping in the LRC Circuit 1 Experiment 2: Oscillation and Damping in the LRC Circuit Introduction In this laboratory you will construct an LRC series circuit and apply a constant voltage over it. You will view the voltage drop over the various elements of the circuit with the oscilloscope. You must change the order of the circuit elements in order to avoid shorting your circuit, but you will only construct one type of circuit throughout this experiment (LRC series). Also, this laboratory does not introduce much new physics to you since many of these topics have been covered in the previous two experiments. On the other hand, this experiment contains several new definitions and a more complicated differential equation, which result in a longer mathematical analysis. 1 Physics 1.1 Review of Kirchhoff’s Law Kirchhoff’s Law states that in any closed loop of a circuit the algebraic sum of the voltages of the elements in that loop will be zero. “Algebraic” simply means signed. Elements in the circuit may either increase (add) voltage or drop (subtract) voltage. 1.2 Voltage Drops Over Various Circuit Elements Resistors, capacitors and inductors have well known voltage drops at direct current (DC) flows through those elements. Ohm’s Law describes that the voltage drop across a resistor is proportional to the current and the resistance: V R = IR (1) The voltage drop across a capacitor is proportional to the charge held on either side of the capacitor. The charge is not always useful in equations mainly in terms of current, but luckily the charge on a capacitor is the integrated current over time: V C = Q C = 1 C Idt ! (2) An inductor is a tightly wound series of coils through which the current flows. A fairly uniform magnetic field is created on the interior of these coils. If the current changes so does the magnetic field and an induced current is produced. The previous statement is a result of the well-known physical law known as Faraday’s Law. The voltage drop is proportional to the change in the magnetic field and therefore the change in the current: V L = L dI dt (3) Also, the coils in inductors often have non-negligible resistance.
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Experiment 2: Oscillation and Damping in the LRC Circuit 2 1.3 Energy Storage in Capacitors and Inductors Where resistors simply give off energy by radiating heat, capacitors and inductors store energy. The energy stored in each is listed below: E C = 1 2 CV 2 E L = 1 2 LI 2 (4) (5) 2 Mathematical Circuit Analysis 2.1 The LRC Series Cricuit In Figure 1 below the circuit you will later construct is shown. Using Kirchhoff’s Law we have: V S + V L + V C + V R = 0 (6) Figure 1 LRC circuit for this experiment Using Equations 1, 2 and 3 in Equation 6 results in: V S ! L dI dt !
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