E13e Switching Processes and Damped Oscillations

Size: px

Start display at page:

Download "E13e Switching Processes and Damped Oscillations"

Harry Sparks
6 years ago
Views:

1 Fakultät für Physik und Geowissenschaften Physikalisches Grundpraktikum E13e Switching Processes and Damped Oscillations Tasks 1. To familiarize yourself with the computer-supported setup PA, measure various time dependent output voltages from a function generator. Determine the frequency and amplitude of the voltages using the cursor measurement-system.. Measure the time dependence of currents and voltages when switching on or off various R and RL series circuits. alculate the characteristic parameters of the circuit elements from the measured time constants. 3. Measure the free oscillations of a RL series circuit. Determine frequency f and damping of the oscillation. By using a variable ohmic resistor tune to the aperiodic limiting case. Literature Physics, P. A. Tipler, 3rd Edition, Vol., 3-, 6-8, 8-4 Physikalisches Praktikum, 14. Auflage, Hrsg. W. Schenk, F. remer, Elektrizitätslehre, 3.3, 4.1 (in German) Accessories Analog-to-digital converter PA with software, connection panel, function generator, laboratory power supply, resistors, capacitors, coils, digital multimeter ey Aspects for Preparation - Time dependence of the charging/discharging of a capacitor - Time dependence of the coil voltage during charging/discharging - Differential equation of the harmonic oscillator, eigenfrequency - Differential equation of the RL series circuit, eigenfrequency, quality factor, damping constant, logarithmic decrement, solutions for the oscillating case, aperiodic limiting case, creep case 1

2 Remarks The aim of this experiment is the study of time-resolved switching on/off processes occurring in R and RL series circuits. Moreover, free oscillations of a RL series circuit should be investigated. The latter circuit is modelled by a linear homogeneous differential equation of. order that is known from the mechanics of the damped harmonic oscillator, but has also broad applications in optics, atomic and molecular physics. For preparation, use irchhoff s laws to set up the relevant differential equations describing the circuits and verify the following solutions for switching on/off processes as well as damped oscillations. Switching on/off of a R series circuit (see circuits below) Switch-on time-function (charging) [time constant τ R = R] U ( ) exp t I t = R R, t U ( t) = U 1 exp R Switch-off time-function (discharging) I (t) = U exp t R R, U ( t ) = U exp t R Switching on/off of a RL series circuit (see circuits below) Switch-on time-function [time constant τ RLE = L/(R+R Sp)] U + R RSp ISp( t) = 1 exp t, L R USp( t) = U 1 1 exp t R + R Sp L Switch-off time-function [time constant τ RLA = L / ( R+R Sp+R p )] U + + R RSp Rp ISp( t) = exp t, L R + Rp + Rp USp( t) = U exp t L

3 Free damped oscillations Oscillation [ ω o > δ, δ =R/L] - U ( ) = e t t U (cos t + sin t ) or ( ) o - t U sin ( ) t = U e t + with tan Aperiodic limiting case [ω o = δ ] - t U ( t ) = U e ( 1 + t ) reep [ω o < δ ] (U : terminal voltage, : damping constant) tanh - o t - t U ( t) = U e 1 - cosh - o t 1- o / Hints to the experiment All voltages must be limited to a maximum of U < 10 V. The following circuits must be set up in a voltageless state and have to be controlled by the supervisor before use. The time dependent electric voltages are digitized by the PA interface, an analog-to-digital converter (AD). Via an USB interface the data are transmitted to the P and are stored in the software PA. The sampling rate and other settings are adjusted via the software. The measurement conditions are different for the various tasks and various values of the circuit elements. Adjust the measurement parameter in such a way that the time curve can be evaluated with highest precision possible in this experiment. The optoelectronic relay of the PA interface is used to switch the circuits. To this end the numbering of the inputs has to be taken into account (see sketch to the right). In the initial state inputs 0 and 1 are connected, whereas after activation of the relay that occurs automatically in the course of the measurement process, a connection between 0 and is established. Inputs and relay circuit of the PA (schematic) 3

4 Get to know the setup onnect the output (OUTPUT 0-10 V pp, 50 ) of the function generator with the input (H 1) of the PA interface. Measure the time dependence of a sine and a triangular voltage. Determine the frequency (or period) and the amplitude using the cursor system of the PA software. R series circuit Discharging As capacitance an electrolytic capacitor is used; therefore, during setup of the circuit pay attention to the correct polarity. The capacitance X is unknown and should be determined. To this end choose ten values of the resistor decade between R = 0.9 k and R = 9 k, determine the time constants from the time dependent voltage U (t) and find X by linear regression of the time constants. harging In order to determine the unknown value of the resistance R X, use the capacitor from the previous task. Measure the switch-on time-curve I(t)=U R(t)/R. Export the data into Origin and determine the time constant R by linear regression of the linearized graph or by fitting an exponential function to the data. Use the value of the time constant to calculate R X. RL series circuit Switch-on process hoose values R = 100 or R = 00 at the decade resistor for the determination of the inductance (L 1, L or L 3) of one of the available coils. Measure the switch-on time-function of the current I(t)=U R(t)/R using the voltage U R(t). In order to determine RL,in, evaluate the measured curve either with the cursor system in PA or with an appropriate graphic analysis. 4

5 Switch-off process For the circuit to the right use resistances R P = 0 and R = 00 (decade resistor). Evaluate the time function U Sp(t) for the determination of the time constant RL,out graphically or by linear regression. RL series circuit For the measurement of the free oscillations of a RL circuit use two known, but different values of the capacitance (important: Osc). Determine the eigenfrequency and the damping constant with the cursor system of the PA software. From these values calculate the inductance used in the experiment and compare to the result of the previous tasks. Software PA The software PA allows for the adjustment of the measurement parameters of the PA interface, it facilitates the transmission of the recorded values to the P and serves for the analysis and storage of the data. Data are recorded on up to four selectable channels. The measured voltages of these channels are shown on a numerical display. For the measurement the sampling rate (number of measurements per second) and the number of measurement points must be adjusted. Take into account that the UI des Programms PA maximum sampling rate is given by 10 5 /number of channels. The voltage range is fixed to ±10 V. The digital resolution is 16 Bit. The switching of the optoelectronic relay integrated in the PA interface is controllable from the program. The recorded data are shown in a table and in a diagram. The export of the data for further analysis is possible in an ASII format. Within the diagram measurements can be directly made with a cursor system. 5

Coupled pendulums and degree of coupling

Fakultät für Physik und Geowissenschaften Physikalisches Grundpraktikum Me Coupled pendulums and degree of coupling Tasks. Measure for three different positions of the coupling spring: a) the oscillation