## AC Circuits

#### Purpose

To build a low pass filter using a capacitor and resistor in series and to investigate how the filter response as a function of the frequency of the input signal.

#### Objectives

- To learn how to use of a digital oscilloscope
- To calculate the impedance of a AC circuit or a resistor and capacitor in series
- To learn the relation between the voltage across each element in an AC circuit of R and C element in series.
- To find out the dependence of the voltage across the C element as a function of the frequency of the input signal

#### Equipment

- Digital Oscilloscope Tektronix TDS 2001C
- Function Generator
- Breadboard, resistors and capacitors
- 3 BNC cables, 1 banana-banana plug cable

#### Definitions

A capacitor in an AC circuit has capacitive reactance of:

An inductor in an AC circuit has inductive reactance of:

#### Activity 1. RC Low Pass Filter

###### Theory

We built a low-pass filter by connecting a resistor and capacitor in series. The impedance of the circuit is:

If the current in the circuit is given by , the maximum voltage across is:

The maximum voltage across the capacitor is:

The ratio between the two then is given as:

or

When the frequency is zero the ratio is simply 1. When the frequency becomes very large (), the limit of the ratio goes to zero. The cut-off frequency is that frequency for which the ratio is one half:

###### Experimental Setting

Use a 1.0-kΩ resistor and a 0.1-μF capacitor to connect them in series to the Function Generator and and turn the power on.