Reference architecture of distributed database

Lab 6: RC Circuits Please read through this lab carefully. There is no one correct way to set up your circuits, this is meant to be a guide. Do not rush through the lab. Your goal in your lab write up is to provide the reader a clear explanation of what you did in the lab and clear understandable tables.

Introduction In this experiment we will measure the discharging behavior of a resistor capacitor circuit. Resistors and capacitors are key elements in many electrical circuits. They are used in camera flashes, defibrillators, power supplies to convert the alternating voltage of generated power into direct current voltage for circuit applications. They are used in "spike removers" or "surge protectors" that safeguard computer equipment from power surges. The list goes on. Understanding how resistors and capacitors work separately and in combination is fundamental to a better understanding of common electrical circuits.

Learning Objectives

• To develop an understanding of the behavior of RC circuits

• To understand the concept of a time constant and use it to find the capacitance

• To be able to analyze non-linear data.

Theory

An RC circuit consists of a resistor and a capacitor wired in series (see Fig. 1). In most common electronic devices, RC circuits charge and discharge very quickly, requiring a fast measuring device such as an oscilloscope. Some RC circuits, like those in power supplies, have capacitors with very large capacitances. These require much longer to charge and discharge,

making it possible to use a slower measuring device. We will use a voltage meter and a stopwatch to measure the time and voltage drop of the discharging capacitor.

Capacitors are nonlinear devices: the rate at which they charge, and discharge is a function of the amount of charge on the capacitor. When charging, the larger the amount of charge on the capacitor plates the slower it will increase its charge. When discharging, the more charge on the capacitor, the faster the charge will decrease. The mathematical representation that describes the charging behavior is:

(1)

(2)

Lab 6: RC Circuits, Page 2 of 9

where Q(t) is the charge on the capacitor at any time, t is the most charge the capacitor can hold, and τ is the “time constant” of the circuit, which governs how quickly the charging and discharging occur. Note that for this simple circuit, when the current is zero, Ohm’s Law states that the voltage across the resistor is zero. But the battery is still in the circuit, so its voltage must exist somewhere in the circuit – it is all across the capacitor. This tells us that the maximum voltage across the capacitor is ε and therefore, using Q = CV, we know that the maximum charge on the capacitor is Qmax = Cε

Since the voltage across the capacitor plates is directly proportional to the charge V = Q/C, we note that the voltage across the capacitor as a function of time is given by:

V(t) = ε (1-e-t/τ) charging (3)

These expressions describe the charging behavior of the RC circuit. When the capacitor is discharging, the voltage across the capacitor as a function of time is described by the relation:

V(t) = V0e-t/τ discharging (4)

Where V0 is the voltage across the capacitor at t = 0, when the capacitor has just started discharging. This is what we will be measuring in this lab.

Using a voltmeter placed across the capacitor, we can capture voltage vs. time curves for charging and discharging. They will look something like the diagram below. We will be measuring the red (dashed) discharging portion of the graph.

Figure 2. Graph showing typical charging and discharging voltage curves, for a time constant of 60 seconds.

Procedure You will be using your 9 V batteries for the power supply. τ

Lab 6: RC Circuits, Page 3 of 9

Read the capacitor label to find out the capacitance of the capacitor. This is an estimate of the actual value. You will determine the actual capacitance as part of the experiment. Calculate what the time constant should roughly be from your values of resistance and capacitance.

Assemble the following circuit. Note that because of the type of capacitor we are using, you must have the longer lead connected to the positive side of the battery.

Setup 1

• Because you might not have a switch in your kit, consider the switch is closed when you connect the negative wire to the capacitor. We will not be charging through a resistor, so the capacitor will reach battery voltage very quickly.

• When the switch is open (you have disconnected the negative wire from the capacitor) the battery is not in the circuit and charge is free to leave the capacitor. The capacitor will discharge over time.

• • In the picture above black wire on the right will serve as the switch

Lab 6: RC Circuits, Page 4 of 9

• Connect your voltmeter across the capacitor with the range set to 20 V. It will be useful to use the alligator clip wires to connect to the capacitor to the voltmeter.

•