{"id":8689,"date":"2021-08-12T22:48:22","date_gmt":"2021-08-12T22:48:22","guid":{"rendered":"https:\/\/liquidinstruments.com\/?p=8689"},"modified":"2025-06-26T04:14:08","modified_gmt":"2025-06-26T04:14:08","slug":"transient-analysis-of-a-capaictor","status":"publish","type":"post","link":"https:\/\/liquidinstruments.com\/coursework\/transient-analysis-of-a-capaictor\/","title":{"rendered":"Intro to circuit analysis lab tutorial","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

This lab tutorial discusses a typical undergraduate electronics lab exercise and how it can be effectively conducted using Moku:Go and its Windows and macOS app while teaching the fundamentals of charging and discharging capacitors within a circuit. This lab was created in conjunction with the University of Detroit-Mercy.<\/p>\n

\"University<\/p>\n

\n

Moku:Go<\/h2>\n

\"Moku:Go<\/em><\/p>\n

Moku:Go combines 15+ lab instruments in one high performance device, with 2 analog inputs, 2 analog outputs, 16 digital I\/O pins and optional integrated power supplies.<\/p>\n

Introduction<\/h2>\n

The oscilloscope is one of the most used tools for electrical engineers throughout their undergraduate education and in their professional careers. This lab is designed to introduce the oscilloscope and programmable power supplies to undergraduates in intro-level circuit analysis courses. You will be using Moku:Go to complete this lab which covers the charging and discharging transients of a capacitor. Figure 1 below shows an image of what measurement in Moku:Go\u2019s Oscilloscope looks like.<\/p>\n

The purpose of this lab is not only an introduction to an oscilloscope but an introduction to the charging and discharging of capacitors. Capacitors are one of the fundamental components in circuits and understanding their various properties is vital to being a successful engineer. One of the most well-known properties of capacitors is that they can store energy in the form of a voltage difference across their plates. However, it takes a non-zero amount of time for this energy to be stored in the capacitor, which is actually a very useful feature when designing timing circuits or power control circuits. The time it takes for a capacitor to be charged to a specified voltage is further studied in this lab tutorial.<\/p>\n

\"Figure<\/p>\n

Figure 1: Oscilloscope Image<\/em><\/p>\n

Pre-lab Exercise<\/h2>\n

1<\/h4>\n

The first exercise is to become familiar with the expression for a charging capacitors transient voltage. Figure 2 below shows a circuit with a charging capacitor and a switch that closes at t = 0s. Using KVL, solve for the voltage across the capacitor VC(t).<\/p>\n

Hint: recall the equation for current through a capacitor i=C(dv\/dt)<\/em><\/p>\n

\"Figure<\/p>\n

Figure 2: Charging Capacitor Design<\/em>
\n\"Solution\"<\/p>\n

This exercise is important for developing fundamental engineering skills like deriving equations for a circuit from KVTL to understand how it will operate under test.<\/em><\/p>\n

2<\/h4>\n

Repeat the previous exercise, except now for a discharging capacitor. Figure 3 below shows a circuit with a discharging capacitor and a switch that opens at t = 0s.<\/p>\n

\"Figure<\/p>\n

Figure 3: Discharging Capacitor Diagram
\n\"Solution\"
\n<\/em><\/p>\n

This exercise is important for developing fundamental engineering skills like deriving equations for a circuit from KVL to understand how it will operate under test. It may be useful to have students derive this formula using various combinations of R and C in series or parallel.<\/em><\/p>\n

3<\/h4>\n

Use the following values for the charging circuit in Figure 2. Find VC when t = 1ms<\/p>\n