* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 10. RLC Circuit
Regenerative circuit wikipedia , lookup
Standing wave ratio wikipedia , lookup
Wave interference wikipedia , lookup
Integrating ADC wikipedia , lookup
Radio transmitter design wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Negative resistance wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Loading coil wikipedia , lookup
Spark-gap transmitter wikipedia , lookup
Power MOSFET wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Index of electronics articles wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Electrical ballast wikipedia , lookup
Rectiverter wikipedia , lookup
Zobel network wikipedia , lookup
Oscilloscope wikipedia , lookup
Network analysis (electrical circuits) wikipedia , lookup
Tektronix analog oscilloscopes wikipedia , lookup
Oscilloscope types wikipedia , lookup
10. The RLC Circuit Objective: Use the oscilloscope to study the decay and oscillation of an RLC circuit Background: An RLC circuit is one in which a resistor, an inductor, and a capacitor are connected in series. If the initial potential difference on the capacitor is V 0 and the initial current is zero, the potential difference at all time is given by V V0 e t cos t where 2L R 02 1 0 2 1 LC These apply provided the condition 0 1 is satisfied, which can be written as R Rc 2 L C where Rc is the resistance for critical damping. t It follows that ln V ln V0 Also 1 R2 LC 4 L2 2 The charging of the capacitor and its subsequent discharge can be accomplished by connecting a square wave voltage generator in series, choosing the frequency to be sufficiently low so that the charging and discharge are essentially complete during each half period of the wave. Procedure: Set up: 1. Note the following parameters for the solenoid used: L 63 mH , R 76 2 2. Connect the function generator in series with a variable resistor, a solenoid, and a variable capacitor. Connect also the CH1 input of the oscilloscope to measure the voltage from the generator. The circuit is shown in the figure. Note that the black end of the cable from the function generator is connected with the alligator end of the cable to the oscilloscope. 3. Select square wave with frequency of about 20Hz on the function generator with amplitude half way between minimum and maximum. 4. A square wave should appear on the oscilloscope screen. (If not, press the “autoset” button.) 1 hook red Function generator oscilloscope black 50Ω `-` Alligator CH1 5. Reconnect the hook end of the cable to the oscilloscope to the capacitor. Select 0.025 μF on the capacitor box and 200Ω on the resistance box. Small oscillations should be visible on the top and bottom parts of the square waves. hook red Function generator 50Ω oscilloscope black Alligator CH1 6. Use position controls and scale controls on the oscilloscope to clearly display a number of oscillations at the bottom of the square wave, taking up almost a full screen. PART 1 Decay of amplitude with time Objective: Determine the inductance by measuring in the exponential factor 1. With the capacitor box set at 0.025 μF and the resistor box at 200Ω, measure and tabulate the voltage V on the capacitor at five successive peaks as well as the time t when the peaks occur. This can be achieved using Cursors 1 and 2 in the positions indicated. 2. Plot ln V against t and obtain from the slope of the best fit straight line 3. Calculate the inductance L from the slope, using for R the sum of the resistance in the box, the resistance of the solenoid, and the 50Ω resistance of the function generator. 4. Repeat 1 through 3 using 400 Ω in the resistor box. 2 PART 2 Dependence of frequency on capacitance Objective: Determine the inductance by measuring the frequency at various capacitances 1. Set the resistance to zero on the resistor box. 2. Vary the capacitance from 0.01µF to 0.05 µF in five steps, measuring the frequency of the oscillations in each case. The positions of Cursors 1 and 2 for this measurement are as shown. 3. Plot 2 versus 1 C and obtain the slope from the best fit straight line. 4. Calculate the inductance L from the slope. Concluding steps: 1. Find the average values of the inductance determined by the above procedures and compare it with the value noted at the beginning of the experiment. 2. Calculate the critical resistance for C 0.025F and L 63mH and verify this by increasing the resistance in the box so that oscillations cease to be visible. 3