RC and RL Circuits - Electronics - Laboratory | PHY 440, Lab Reports of Basic Electronics

Download RC and RL Circuits - Electronics - Laboratory | PHY 440 and more Lab Reports Basic Electronics in PDF only on Docsity! RC and RL Circuits – Page 1 RC and RL Circuits RC Circuits In this lab we study a simple circuit with a resistor and a capacitor from two points of view, one in time and the other in frequency. The viewpoint in time is based on a differential equation. The equation shows that the RC circuit is an approximate integrator or approximate differentiator. The viewpoint in frequency sees the RC circuit as a filter, either low-pass or high-pass. For each experiment starting with 2, make a copy of the screen showing input and output waveforms and place it in your lab notebook. Experiment 1, A capacitor stores charge: Set up the circuit below to charge the capacitor to 5 volts. Disconnect the power supply and watch the trace decay on the ‘scope screen. Estimate the decay time. It will be shown that this decay time, τ = RC, where R is the resistance in ohms and C is the capacitance in farads. From this estimate calculate an approximate value for the effective resistance in parallel with the capacitor. (This resistance is the parallel combination of the intrinsic leakage resistance within the capacitor and the input impedance of the ’scope.) [Ans.: about 1 s] Next, replace the 0.047 µF capacitor by a 1000µF electrolytic capacitor [Pay attention to the capacitor polarity!] and watch the voltage across it after you disconnect the power supply. While you are waiting for something to happen, calculate the expected decay time. Come to a decision about whether you want to wait for something to happen. Act according to that decision. scope 0.047 µF 5V Figure 1: Capacitor charging circuit. RC and RL Circuits – Page 2 Experiment 2, The RC integrator in time: Consider the RC circuit in Figure 2 below: In lecture you learned that this circuit can be described by a differential equation for q(t), the charge on the capacitor as a function of time. It was shown that a solution for the voltage on the capacitor, VC = q(t)/C, consistent with no initial charge on the capacitor, is: ! V C =V 0 (1" e "t /# ) where τ = RC and V0 is the initial voltage. Now build the circuit, replacing the battery and switch by a square wave generator. (Note: The square wave generator has positive and negative outputs, but this is the same as switching the battery with an added constant offset and a scale factor.) Set the square wave frequency to 200 Hz, and observe the capacitor voltage. 10k VC Scope A Scope B 0.047 µF 1V Figure 2: RC Circuit. t t τ V+ 0 V- Figure 3: Square Wave and Integrator Output. RC and RL Circuits – Page 5 Next, do the “half-voltage” calculations and measurements, as for the RC low- pass filter. RL Circuits This part of the lab uses a 27 mH inductor and resistors. Experiment 6, Real inductors – the ugly truth: Use an ohmmeter to measure the DC resistance of the inductor. Write the answer in your lab notebook. Experiment 7, Real inductors – arcs and sparks: Set up the circuit below. Once equilibrium is established, after the switch is closed, there remains a voltage across the inductor. Why should this be? Disconnect the power supply abruptly and carefully watch the voltage across the inductor. Connect, disconnect, connect, disconnect … You should see spikes that exceed the original supply voltage. How can this be? How can you get more voltage from the inductor than the power supply voltage? Is there a violation of a Kirchoff law? Is there a violation of conservation energy? Experiment 8, The RL differentiatior: Replace the power supply and switch above with a square wave generator. Scope A Figure 6: RL Circuit. scope 27 mH 5V 150Ω Scope B 27 mH 150Ω Figure 7: RL Differentiator. RC and RL Circuits – Page 6 Calculate time constant τ = L/R. Remember to include the resistance intrinsic to the inductor in R as well as a 50Ω resistance contributed by the pulser. Measure the time constant on the DPO and compare with the calculated value. Experiment 9, The RL integrator: Design an RL integrator and verify its operation on the DPO.