Download 10. RLC Circuit

10. The RLC Circuit
Objective: Use the oscilloscope to study the decay and oscillation of an RLC circuit
Background:
An RLC circuit is one in which a resistor, an inductor, and a capacitor are connected in series. If the initial
potential difference on the capacitor is V 0 and the initial current is zero, the potential difference at all time is
given by
V  V0 e

t

cos t
 
where
2L
R
  02 
1

0 
2
1
LC
These apply provided the condition  0  1  is satisfied, which can be written as
R  Rc  2
L
C
where Rc is the resistance for critical damping.
t
It follows that
ln V  ln V0 
Also
1
R2
 

LC 4 L2

2
The charging of the capacitor and its subsequent discharge can be accomplished by connecting a square wave
voltage generator in series, choosing the frequency to be sufficiently low so that the charging and discharge are
essentially complete during each half period of the wave.
Procedure:
Set up:
1. Note the following parameters for the solenoid used: L  63  mH , R  76  2
2. Connect the function generator in series with a variable resistor, a solenoid, and a variable 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.
3. Select square wave with frequency of about 20Hz on the function generator with amplitude half way
between minimum and maximum.
4. A square wave should appear on the oscilloscope screen. (If not, press the “autoset” button.)
1
hook
red
Function
generator
oscilloscope
black
50Ω
`-`
Alligator
CH1
5. Reconnect the hook end of the cable to the oscilloscope to the capacitor. Select 0.025 μF on the
capacitor box and 200Ω on the resistance box. Small oscillations should be visible on the top and bottom
parts of the square waves.
hook
red
Function
generator
50Ω
oscilloscope
black
Alligator
CH1
6. Use position controls and scale controls on the oscilloscope to clearly display a number of oscillations at
the bottom of the square wave, taking up almost a full screen.
PART 1 Decay of amplitude with time
Objective: Determine the inductance by measuring  in the exponential factor
1. With the capacitor box set at 0.025 μF and the resistor box at 200Ω, measure and tabulate the voltage
V on the capacitor at five successive peaks as well as the time t when the peaks occur. This can be
achieved using Cursors 1 and 2 in the positions indicated.
2. Plot ln V against t and obtain  from the slope of the best fit straight line
3. Calculate the inductance L from the slope, using for R the sum of the resistance in the box, the
resistance of the solenoid, and the 50Ω resistance of the function generator.
4. Repeat 1 through 3 using 400 Ω in the resistor box.
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PART 2 Dependence of frequency on capacitance
Objective: Determine the inductance by measuring the frequency at various capacitances
1. Set the resistance to zero on the resistor box.
2. Vary the capacitance from 0.01µF to 0.05 µF in five steps, measuring the frequency of the oscillations in
each case. The positions of Cursors 1 and 2 for this measurement are as shown.
3. Plot  2 versus 1 C and obtain the slope from the best fit straight line.
4. Calculate the inductance L from the slope.
Concluding steps:
1. Find the average values of the inductance determined by the above procedures and compare it with the
value noted at the beginning of the experiment.
2. Calculate the critical resistance for C  0.025F and L  63mH and verify this by increasing the
resistance in the box so that oscillations cease to be visible.
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