Title : RC circuit

Apparatus :

     Science Workshop Interface 750

      Voltage sensor ( PASCO CI-6503 )

      Capacitors ( )

      Variable resistor 

      Transistor Basic Unit

      Power Relay

      12V Electric light bulb

       Low Voltage Power Supply

Objective :

Study the charging and discharging processes in RC circuit

Estimate capacitance from the half-life of a capacitor in RC circuit

Application of RC circuit 

Theory :

A capacitor is a device which is used to store electric charge.

The measure of the extent to which a capacitor can store charge is called Capacitance. It is defined by :

In words, capacitance equals the charge required to cause unit change in the potential of a conductor.

(a)        Charging a capacitor

        Initially, the charged stored in the capacitor is zero and the initial current is

        At t > 0, the charging current is I and the instantaneous charge stored in the capacitor is Q.

       By Loop theorem,

        During the charging period, I and Q are related by

        Solving the above two equations, we have

        The p.d. across the capacitor is

        The stored charge and the p.d. across C increase exponentially. ( At first, the capacitor is easy to charge because there is very little charge on the plates. But as charge accumulates on the plates, the voltage source must "do more work" to move additional charges onto the plates because the plates already have charge of the same sign on them. As a result, the capacitor charges exponentially, quickly at the beginning and more slowly as the capacitor becomes fully charged. ) 

        V_C rises rapidly from zero and slowly approaches its maximum value.   

        The quantity R C has the dimensions of time and is called the time constant of the circuit.

 (b)       Discharging a capacitor

        Initial the capacitor is  fully charged.

        At t > 0, the discharging current is I and the instantaneous charge is Q.

       By Loop theorem,

        I and Q are related by

    The negative sign is necessary because Q is decreased with time t , 

       is negative and I is positive.

    Solving eq (3) and (4), we have

    The p.d. across the capacitor is

   In this experiment, a voltage sensor is used to record the voltage across the capacitor,       

    and  therefore, the variation of the charge stored in the capacitor is indirectly recording.

 (c)       Charging and Discharging a capacitor continuously

   In order to show charging and discharging a capacitor continuously, a square wave is used 

    as shown in the following diagram.

    Figure 1

Procedure :

Hardware setup :

1.  Connect the Interface to the Computer, turn on 

       the interface, and turn on the computer.

2. Connect the Voltage Sensor to the interface

3. Connect the function generator ( OUTPUT ports 

     on the interface ) directly across the RC circuit 

    and voltage sensor from analog channel A across 

    the capacitor as shown in the following diagram.

     Click to play the PPT file

   Use the "Output" feature of the interface to supply a voltage to the resistor - capacitor circuit. Use the Voltage Sensor to measure the voltage across the capacitor as it charges and discharges.

Software setup :

4.  The signal generator is set to output a 5 volt,

   "positive only" square wave at 0.40 Hz.

   The Signal Generator is set to ' Auto' so it will start and stop automatically.

Data Recording 

( charging and discharging the capacitor )

Data Analysis :

Charging and discharging a capacitor in RC circuit

Estimate capacitance of a capacitor in RC circuit

Application of RC circuit 

Discussion :

1.  What are the precautions of this experiment ?

2.  What are the difficulties in performing this experiment using 

       traditional apparatus ?

3.  Is the calculated capacitance equal to the  marked value 

       shown on the capacitor ?

4.  Discuss the advantages of using data-logging system in

      doing this experiment.