| Introduction |
Procedure1. Observe Current and Applied VoltageBegin by wiring the capacitor, inductor and resistor in series with the frequency generator, as shown below.
Measure the voltage across the frequency generator with channel 1 of the oscilloscope, and use channel 2 to measure the voltage across the resistor. Notice that the above circuit is wired so that the ground connections of both scope channels are connected to the ground of the frequency generator. Note: oscilloscopes do not measure current directly (like an ammeter). In this case, we are measuring the voltage across the resistor, which is in phase with the current. By displaying both channels 1 and 2 on the same plot, we can observe the phase difference between current and applied voltage. Preparation
Your scope display should look something like this:
The larger-amplitude trace is the applied voltage, which has a peak-to-peak value of about 1 volt, as expected. The smaller amplitude voltage is the voltage across the resistor VR. Since time is plotted on the horizontal axis and increases to the right, it is clear that VR always reaches its maximum before the applied voltage. Thus, current leads voltage in this case. Verify Component ValuesUsing one of the LCR meters, measure and record accurate values for your inductor, capacitor and resistor. The nominal values are: Resistor: R = 4.7kΩ (yellow-purple-red) Capacitor: 0.01μF Inductor (large coil): 0.88 H Amplitude vs. Peak-to-Peak ValuesRecall that your oscilloscope reports peak-to-peak values, which for a sine wave is twice the amplitude Vm where V(t) = Vm sin(ωt). Make sure you understand this distinction by filling in the information on the data page. 2. ResonanceAdjust the frequency until a maximum current is achieved. In this case, voltage and current should be in phase. Your trace should look something like:
Note that there are two traces in the above plot - it looks like one trace because they fall right on top of each other. Current is clearly in phase with applied voltage when the circuit is driven at resonance. Actually, if you look closely, you can see that the trace for VR is a bit smaller. This is because of the finite resistance of the coil (62.5Ω) which is small compared to R (4.7kΩ) but not negligible. Record the resonant frequency, and compare to the predicted value using component values measured with the LCR meter. Using the Oscilloscope to Determine Current Values If you have wired your circuit according to the diagram above, then channel 2 measures the voltage across the resistor VR. You can use Ohm's law to determine the current that flows in your circuit.
Investigate Frequency Dependence Follow the above steps to investigate the current and impedance at 1000 Hz and 2500 Hz. In each case, determine VR (which will now be substantially less than the applied voltage amplitude. You should then be able to determine the impedance (which will be substantially more than R). For example, suppose VR is 0.5V at resonance, and 0.225V at 1000 Hz. Then going from resonance to 1000 Hz increases Z by a factor of (0.5/0.225). Your observations should agree with calculations using measured component values. To observe the phase between current and applied voltage, turn the display for channel 1 back on. Record your observations on the data page. |