3. What is the maximum charge for the capacitor in this experiment? 4. What are some factors that could account for the percent difference between the stated and experimental values?
Data Studio file: 09B-LRC Circuit.dsEquipment List2 Banana Plug Patch Cord1 Voltage Sensor1 AC/DC Electronics Laboratory1 PASCO 750 InterfaceConnect the voltage Sensor to the interface on channel A IntroductionThe purpose of this activity is to study resonance in an inductor-resistor-capacitor circuit (LRC circuit) by examining the current through the circuit as a function of the frequency of the applied voltage. Determine what happens to the amplitude of the current in the LRC circuit when the frequency of the applied voltage is at or near the resonant frequency of the circuit. Use the ‘OUTPUT’ feature of the PASCO 750 Interface to apply voltage to the circuit. Use the Voltage Sensor and Data Studio to measure the voltage across the resistor in the circuit as the frequency of the voltage is changed. The voltage measured across the resistor is related to the current through the resistor by . Also, investigate the phase relationship between the applied voltage and the resistor voltage as you vary the frequency.When a vibrating mechanical system is set in motion, it vibrates at its naturalfrequency. However, a mechanical system can be forced to vibrate at adifferent frequency. The amplitude of vibration, and hence the energytransferred to the system, depends on the difference between the naturalfrequency and the frequency of forced vibration. The amplitude becomes verylarge when the difference between the natural and forced frequency becomesvery small. This is known as resonance and the natural frequency of the system is sometimes called the resonant frequency. At resonance, relatively little energy is required to get a large amplitude. One example of resonance is when a singer’s amplified voice is used to shatter a glass. Electrical resonance is analogous to mechanical resonance. The energy transferred to a system is a maximum at resonance. The amplitude of the AC current (Io) in a series LRC circuit is dependent on the amplitude of the applied voltage (Vo) and the impedance (Z).Since the impedance depends on frequency, the current varies with frequency:
where XL= inductive reactance = L, XC= capacitive reactance = , R= resistance, and = angular frequency = 2f (f = linear frequency). The current will be maximum when the circuit is driven at its resonant frequency: One can show that, at resonance, XL= XCand thus the impedance (Z) is reduced to R. Atresonance, the impedance is the lowest value possible and the current will be the largest value possible.SetupSet up the PASCO 750 Interface and the computer and start DataStudio.Connect the Voltage Sensor into the interface. Connect banana plug patch cords