In this experiment, our purpose is to analyze the resonance behavior of the LRC circuit. It is know that the circuit shows resonance under a particular driving frequency and this phenomenon is utilized widely in our everyday life. Here, from the most fundamental form of LRC circuit, we try to show how the magnitude of resonance frequency is related to the inductance, capacitance and resistance of the circuit.
Moreover, even though for the most of the case it is a sine wave that is applied to the circuit, we try another form of square for the circuit. From the graph which shows how the resistor voltage develops with respect to the time, we analyze how the behavior differs from that in which the sine wave was applied to the circuit.
Ⅱ. Theoretical Basis
1.The Behavior of LRC Circuit
2. The Resonance of LRC Circuit
Ⅲ. Experimental Techniques and Method
Ⅳ. Experimental Data and Analysis
Ⅱ. Theoretical Basis
The Behavior of LRC Circuit
omposed of an inductor, a capacitor, and a resistance connected in a series. Provided that denotes the current, Q denotes the charge in the capacitor and satisfies according to the Kirchhoff’s Rule.
However, the current is the time derivative of the charge. Therefore, the above equation becomes the second-order differential equation of Q with respect to time.
The auxiliary equation for the above differ
For both two parts of our experiments, we composed LRC circuit whose inductance was 0.00144 H, capacitance was 100 μF, and resistance was 20 Ω.
For the first part, we observed how the resistor voltage amplitude changes with respect to the output voltage angular frequency, provided that the output voltage had sine wave as its form. Our angular frequency for sine wave output voltage was increased 200 Hz at each time. From the plot, we could observe that the amplitude maximizes within the range from 2300 Hz to 2700 Hz, but we concluded 2500 Hz as the most probable value due to the symmetry of the plot. However, the theoretically expected value of resonance frequency was 2635 Hz, which makes our experimental data have percentage error of -5.13%.
For the second part, we observed how the resistor voltage would develop with respect to the time if output voltage were in the form of squares with alternating signs. The certain value of output voltage was set to be constant for an interval of 5 milliseconds each. Due to periodically alternating output voltage, we could observe periodically occurring harmonic oscillations in resistor voltage, which also changes in sign with period same as that of output voltage square wave.