Download Lab07_La_Juan

Physics 102
RC Circuits
Phuc La, Juan Guerrero
March 16, 2006
Abstract:
The purpose of this lab is to quantitatively observe the changing voltages and
determine experimentally the validity of Kirchhoff’s Loop Law in an RC circuit.
This laboratory is also used to determine the voltage ratio at the time constant.
Equipment:
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four resistors (100Ω, 985Ω, 10130Ω, 101000Ω)
capacitor (5 μF)
power supply
computer
Pasco Datastudio with voltage sensors
Procedure:
The circuit is set up like the picture:
Picture 01
The capacitor is set to 5 μF
The resistor is 100Ω.
The power supply is set to 6V.
Probe 1, fits in the DIN sockets A, is set up to parallel with the capacitor to
record the voltage across the capacitor.
5. Probe 2, fits in the DIN sockets B, is set up to parallel with the resistor to
record the voltage across the resistor.
6. DataStudio interface is set up to record voltages which change with the
time.
7. The switch connects to B point to discharge the capacitor.
8. The switch connects to A to make RC circuit.
9. Click the Start button on the menu bar of DataStudio and turn on the
power supply.
10. DataStudio records changing voltage and time.
1.
2.
3.
4.
11. Click the Stop button on the menu bar of DataStudio and turn off the
power supply.
12. The experiment repeat steps 7-11 with 985Ω resistor, 10130Ω resistor and
101,000Ω resistor.
Data:
Data is in the excel file which is “Lab07_La_Juan.xls”.
R is 100Ω, the data is “R100” worksheet in the excel file.
R is 985Ω, the data is “R985” worksheet in the excel file.
R is 10,130Ω, the data is “R10,130” worksheet in the excel file.
R is 101,000Ω, the data is “R101,000” worksheet in the excel file.
Analysis:
calculations:
The voltage of power supply is 6.0 V, so Vo = 6.0 V.
R and C are available so the time constant is R*C.
The voltage of the capacitor is
VcapTheo = Vo (1 - e(-t/RC))
t is taken from time column in the excel file.
R, C, t and Vo are substituted in above equation to find the theoretical voltage of
the capacitor at various time.
The voltage of the resistor at various time is
VresTheo = Vo – VcapTheo
graphs:
Graph is in the excel file which is “Lab07_La_Juan.xls”.
R is 100Ω, the data is “R100Graph” worksheet in the excel file.
R is 985Ω, the data is “R985Graph” worksheet in the excel file.
R is 10,130Ω, the data is “R10,130Graph” worksheet in the excel file.
R is 101,000Ω, the data is “R101,000Graph” worksheet in the excel file.
Error analysis:
There are some variations in the data. These variations have come from several
sources:
 Reading errors
 Device variation
 Instructions
 Calculating
Reading error is common error. In the experiment, the data is read from the
device. The device shows a variant number. Therefore the recorded data is an
estimate or average of the fluctuation quantity.
The device used in the experiment also contributed to errors. Each device has a
deviation, so it adds to the affects of the result of the experiment. In the
experiment, there is resistance in wires and devices, so the result is different
from the theory result.
Not following instructions can affect the data in the experiment. If an experiment
is done incorrectly then the, data may come out incorrect. With incorrect data, a
person’s conclusion will be incorrect.
Calculating errors are also made. When the results are rounded off early in
calculations, it affects the following steps. In the experiment, the theoretical
voltage and current are rounded off so when total voltage and current are
calculated they are not going to come out perfect.
In the experiment, there are errors in the results. The different voltage equals the
experimental voltage minuses the theoretical value.
R is 100Ω, the different voltage is in “R100” worksheet in the excel file.
R is 985Ω, the different voltage is “R985” worksheet in the excel file.
R is 10,130Ω, the different voltage is “R10,130” worksheet in the excel file.
R is 101,000Ω, the different voltage is “R101,000” worksheet in the excel file.
Questions:
1. The time constant is
t = RC
Besides, the equation is
V = Vo (1 - e(-t/RC))
It is changed to be
V
 1  e (  t / RC )
Vo
t is substituted into the above equation. It become:
V
1
1  e (  RC / RC ) 1  e 1 1 
Vo
e
So, the average value of
V
Vo
is 1
1
.
e
2. The Kirchoff’s Law is verified because “VcapExp + VresExp” column is
near 6.0 V which is the voltage of power supply.
The variations are from the resistor of the wire. Besides, the capacitor
didn’t discharge after doing the previous experiment.
3. In a parallel RC circuit, the capacitor becomes charged, less current flows
through it and more is left over for the resistor. The above equation
Q = VC
C is a constant. Q is increased so the voltage of the capacitor is increased
with time but not over the voltage of the power supply.
Besides, Ohm’s Law, the below equation is
V = IR
I is increased and R is a constant, so voltage of the equation is increased
but not over the voltage of the power supply.
The power supply is disconnected from the circuit. The charged stored on
the capacitor are free to move thought the resistor toward each other.
The equation is Q = VC. The Q is descreased and C is a constant, so the
voltage of the capacitor is descreased and closes to 0.
The Ohm’s Law has
V = IR
The current through the resistor is descreased and R is a constant. so the
voltage of the resistor is descreased and closes to 0.
Conclusion:
The laboratory shows the charging and discharging rates of the capacitor. In the
series RC circuit, the voltage of the capacitor increased but the voltage of the
resistor descreased. In the parallel RC circuit, the voltage of the capacitor
increased and the voltage of the resistor also increased.
Grade = 100