Download 9. RC Time Constant

9. The RC Time Constant
Objective: Use the oscilloscope to measure the time constant of an RC circuit
Background:
During discharge, the voltage on a capacitor connected to a resistor is given by
V  V0 e

t

where V 0 is the initial voltage and the time constant  is given by
  RC .
Taking natural log:
ln V  ln V0 
t

.
so that a plot of lnV versus t is a straight from the slope of which  can be determined.
Function Generator The charging and discharge can be accomplished by connecting the capacitor to a
function generator that generates a square wave voltage as shown. Charging occurs during the half period when
the voltage is constant at V 0 and discharge occurs during the other half period when the voltage is zero. If the
period is long compared with the time constant, the charging and discharge are essentially complete. The
function generator has internal resistance 50Ω. During the charging phase, it behaves as a battery with 50Ω
internal resistance. During discharge phase, it behaves as a simple 50Ω resistor.
Oscilloscope The oscilloscope is an instrument capable of measuring and displaying time-periodic voltage
signals. It does so by refreshing (triggering) the screen display at the same phase of the periodic signal so that
the display remains stationary. Two signals can be simultaneously displayed using channels 1 and 2, but we will
only use channel 1. We will also use only two menu: the CH1 Menu and the Cursor Menu.
The CH1 Menu is used to shift the position of the display, to expand or contract the display by changing the
scales on the time and voltage axis.
The Cursor Menu is used to set a cursor at the time and voltage coordinates at a selected point. Two points
can be selected using Cursor1 and Cursor 2 respectively. If Cursor 1 is chosen as a reference, then setting a
point at Cursor 2 gives the time and voltage difference between this point and the reference.
Procedure:
Set up:
1. Connect the function generator in series with a resistor and a capacitor. Connect also the CH1 input of
the oscilloscope to measure the voltage from the generator. The circuit is shown in the figure. Note that
the black end of the cable from the function generator is connected with the alligator end of the cable to
the oscilloscope.
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2. Select square wave with frequency of about 200Hz on the function generator with amplitude half way
between minimum and maximum.
3. A square wave should appear on the oscilloscope screen. (If not, press the “autoset” button.)
hook
red
Function
generator
50Ω
oscilloscope
black
Alligator
CH1
Practice Controlling the Screen Display
4. Position Control: In the CH1 Menu, use the vertical and horizontal control buttons to move the
displayed signal up and down.
5. Time scale control: In the CH1 Menu, turn the ‘sec/div’ knob to change the time scale of the display
(Turning up the knob increases the time per division on the screen, causing less number of periods to be
displayed.)
6. Voltage scale control: In the CH1 Menu, turn the CH1 ‘volts/div’ knob to achieve the same purpose as
step 5 for the voltage scale. For fine control, select the “Volts/Div” option in CH1 Menu to ‘fine’.
7. Set start time and voltage reference for data collection: Enter Cursor 1 Menu. Make sure that CH1 is
selected under “Source”. Select the option ‘time’ under “Type”. Use the position knob marked CH1 to
move cursor 1 to the desired time to serve as the start time. Then select ‘voltage’ and use the same knob
move cursor 1 to the desired voltage as reference voltage.
8. Measure time and voltage : From Cursor 2 Menu, select ‘time’ and move cursor 2 to the time to be
recorded. The ‘delta’ entry on the menu is the difference between the cursor 2 time and the cursor 1
time, and is therefore the time elapsed since the start time. Similarly, by selecting ‘voltage’ and moving
cursor 2 to the desired voltage level, the ‘delta’ entry gives the current voltage above the level defined
by cursor 1.
Study the Discharge Phase
9. Set the resistance at 2950Ω so that the total resistance is 3000Ω in the circuit. Note the value of the
capacitance.
10. Monitor the voltage of the capacitor: Remove the hook end of the oscilloscope cable from the function
generator and reconnect it to a lead on the capacitor (the other lead is connected to the alligator end of
the oscilloscope cable). A rising and a falling trace should appear on the screen, corresponding to the
capacitor voltages during the charging and the discharge phases. Adjust the frequency of the oscillator to
ensure that the charging and discharge are essentially complete during each half wave.
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hook
red
Function
generator
50Ω
oscilloscope
black
Alligator
CH1
11. Obtain a good display of the discharge phase: By using the controls described earlier, display only the
discharge portion of the trace so that it more or less fills a full screen. (You may have to adjust the
oscillator frequency slightly to shift the trace horizontally.) The trace should begin at the upper left
corner of the screen and end at the lower right corner. For ease of data taking later, align the zero level
of the square wave with a horizontal dotted grid line.
Cursor 2
Cursor 1
V
t
12. Setting the start time and reference voltage: Using cursor 1, set the start time at the highest point ( top of
the square wave) of the falling trace, and set the reference voltage level at the bottom of the square
wave.
13. Measure time and voltage along the discharge trace: Use cursor 2 to measure the time and voltages of
five points on the trace. To ensure that the same point is measured as you switch from ‘time’ to ‘voltage’
, you might want to choose the points that lie on successive horizontal grid lines. The positions of the
two cursors are illustrated in the figure above.
14. Obtain time constant: Plot ln V against t . Determine the time constant  from the slope of the best fit
straight line.
15. Comparison with theory: Compare  with RC where C is the capacitance indicated on the capacitor,
and R  3000 (The resistance on the box plus 50Ω from the oscillator).
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