Lab Report
Experiment 8: LRC Circuit
Aim
The aim of this experiment is to measure and calculate the resonance frequency in different ways. Meanwhile, there is a requirement to use the apparatus proficiently. For the last part of the experiment, there is a demand to analyze the phenomenon and get a better understanding. Moreover, from this experiment, we can understand the principle of this experiment and learn some circuit knowledge.
Background/ Theory
In the experiment, in an LRC circuit, a resistor(R), an inductor (L) and a capacitor (C) are required to connect in series. Just like the figure shows.
In the experiment, we want to calculate the resonance frequency. We know the current will be maximum when the circuit is driven at its resonance frequency.
In addition, the amplitude I0 of the AC current in a series LRC circuit depends on the amplitude V0 of the applied voltage and the impedance Z, which is a measure of the overall opposition of a circuit to the flow of an electrical current as ,
So we just need to use the apparatus to measure the maximum voltage. As we know, at the resonance frequency, we have XL=XC and the impedance, Z is equal to the resistance R, where Z=R.
Because the capacitative and inductive reactances vary with the frequency of the AC current, the impedance of a circuit containing capacitors and inductors also varies with AC frequency. For a circuit with AC current flowing at angular frequency ω, its impedance is given by
where XL = ωL is the inductive reactance, XC = 1/ωC is the capacitative reactance, R is the resistance, and ω = 2π f ( f is the linear frequency).
Apparatus
• PC with DataStudio installed
• Science Workshop 750 USB Interface Box
• Power Amplifier
• Voltage Sensor
• AC/DC Electronics Lab Board
• LCR meter
• Connecting patch cords
Experimental Procedure
The experimental procedure can be divided into three parts:
Part I: Using a Frequency Scan to Determine the Resonance Frequency
• The first
Aim
The aim of this experiment is to measure and calculate the resonance frequency in different ways. Meanwhile, there is a requirement to use the apparatus proficiently. For the last part of the experiment, there is a demand to analyze the phenomenon and get a better understanding. Moreover, from this experiment, we can understand the principle of this experiment and learn some circuit knowledge.
Background/ Theory
In the experiment, in an LRC circuit, a resistor(R), an inductor (L) and a capacitor (C) are required to connect in series. Just like the figure shows.
In the experiment, we want to calculate the resonance frequency. We know the current will be maximum when the circuit is driven at its resonance frequency.
In addition, the amplitude I0 of the AC current in a series LRC circuit depends on the amplitude V0 of the applied voltage and the impedance Z, which is a measure of the overall opposition of a circuit to the flow of an electrical current as ,
So we just need to use the apparatus to measure the maximum voltage. As we know, at the resonance frequency, we have XL=XC and the impedance, Z is equal to the resistance R, where Z=R.
Because the capacitative and inductive reactances vary with the frequency of the AC current, the impedance of a circuit containing capacitors and inductors also varies with AC frequency. For a circuit with AC current flowing at angular frequency ω, its impedance is given by
where XL = ωL is the inductive reactance, XC = 1/ωC is the capacitative reactance, R is the resistance, and ω = 2π f ( f is the linear frequency).
Apparatus
• PC with DataStudio installed
• Science Workshop 750 USB Interface Box
• Power Amplifier
• Voltage Sensor
• AC/DC Electronics Lab Board
• LCR meter
• Connecting patch cords
Experimental Procedure
The experimental procedure can be divided into three parts:
Part I: Using a Frequency Scan to Determine the Resonance Frequency
• The first