**Circuits**

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. In the first two part of this Unit, you will build RC and RLC circuits, which lay the foundation of filtering, oscillators, and resonance. In the third part, you will explore an application of these circuits by building an EKG.

**Lab 3A: RC Circuits and Damped Oscillation****Lab 3B: Resonance and Q-Factor****Lab 3C: EKG**

**Physics Background**

To review physics laws on mechanics, please check out

**OpenStax texbook.**Here are important Chapters:Please also refer to Wikipedia:**Lab 3A: RC Circuits and Damped Oscillations**

We are going to start with 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.

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.

**Pre-Lab 3A - Damped Oscillation Fitting**

****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 and exponential. Furthermore, when an inductor is introduced, the RC circuit begins to resonate with the inductor introducing a sinusoidal function. Complete the following pre-lab to gain an understanding on how to fit functions to complex data-sets like damped oscillations.

**Lab 3A - RC Circuits**

Study of RC circuits.

**Lab 3B: RLC Circuits and Resonance**

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.

**Pre-Lab 3B - Resonance and Q-factor**

Revisit damped oscillation fitting and Q-factor formulation. Gaussian's are the 1st order approximation to the resonance curve and will therefore be used to fit the data captured in this lab. Please also review the concept of low-pass, high-pass, and band-pass filtering by the passive RC circuits by reading below:

**Lab 3B - Resonance and Q-factor**

**Lab 3C: EKG**

An abbreviation for electrocardiogram, an EKG (ECG) is a device used to detect a heart beat by measuring the voltage oscillations produced by one's heart. These devices use a number of leads to measure the signal produced by the heart, and include both analog and digital filters to limit the noise produced by other electrical sources, such as muscle contractions. Thus professionally build EKG devices have high signal-to-noise ratios. We will try some measures to increase our signal-to-noise ratios with a series of low-pass filters.

**Lab 3C pre-lab**

**Lab 3C - EKG**

**Unit 3 Report - Circuits**

**Unit 3 Report**(Due Friday 14, 2020)