**Circuits - Summer 2023**

Circuits are the an integral part of human life in this day and age. Radios, televisions, phones, computers, etc., are complex circuits. However, they are based on simple physical principles. That is the purpose of this lab, to teach you the basic principles behind circuits. We will also introduce how to use your Arduino and computer as a virtual oscilloscope.

We are going to start with verifying Ohm's law and producing an I-V curve for an LED. Next we will look at a simple RC circuit. We will see a capacitor charge and discharge using this circuit. The timing of the charging is referred to as the RC time constant. In many circuits, a time varying current is present. We observe oscillations in the voltage of these circuits when an inductor is introduced. Since all circuits have some form of resistance and capacitance, it is important to understand the fundamentals of RLC circuits. In this lab we will examine the most basic RLC circuits.

With our knowledge about RC circuits, we will continue to the study of RLC circuits. We will examine the concept of resonance by applying a range of frequencies to our RLC circuit. When a system is on resonance, the amplitude of the oscillations will increase drastically. In mechanical systems this amplitude increase can be very destructive, with a common example shown being the collapse of the Tacoma Narrows Bridge due to the wind. In a much less frightening way, this lab will look for the resonance by sweeping over the frequencies applied to an RLC circuit.

When an inductor (L) is added in series to the RC circuit a phenomena known as oscillation begins to occurs. The reason is because the capacitor and the inductor are out of phase in their voltages, therefore they begin to oscillate when supplied with a step function voltage, better known as "ringing." You will study how to create RLC circuits and supply a square wave or step voltage to create this oscillation. In addition, you will determine what effect a resistor has on this oscillation.

We are going to start with verifying Ohm's law and producing an I-V curve for an LED. Next we will look at a simple RC circuit. We will see a capacitor charge and discharge using this circuit. The timing of the charging is referred to as the RC time constant. In many circuits, a time varying current is present. We observe oscillations in the voltage of these circuits when an inductor is introduced. Since all circuits have some form of resistance and capacitance, it is important to understand the fundamentals of RLC circuits. In this lab we will examine the most basic RLC circuits.

****Our study of circuits begins with RC circuits and the measurement of the RC time constant, τ. This time constant is the amount of time required for the capacitor in the RC circuit to charge up to ~63% and conversely, discharge to ~37%. The analytical solution for this circuit is simply an exponential.With our knowledge about RC circuits, we will continue to the study of RLC circuits. We will examine the concept of resonance by applying a range of frequencies to our RLC circuit. When a system is on resonance, the amplitude of the oscillations will increase drastically. In mechanical systems this amplitude increase can be very destructive, with a common example shown being the collapse of the Tacoma Narrows Bridge due to the wind. In a much less frightening way, this lab will look for the resonance by sweeping over the frequencies applied to an RLC circuit.

When an inductor (L) is added in series to the RC circuit a phenomena known as oscillation begins to occurs. The reason is because the capacitor and the inductor are out of phase in their voltages, therefore they begin to oscillate when supplied with a step function voltage, better known as "ringing." You will study how to create RLC circuits and supply a square wave or step voltage to create this oscillation. In addition, you will determine what effect a resistor has on this oscillation.

**Unit 3 Reference Material**

**Additional Circuits Background References**

To review physics laws on mechanics, please check out

**OpenStax texbook.**Here are important Chapters:Please also refer to Wikipedia: