Physics 222 RC Circuits Oscilloscope Lab
Physics 222 RC Circuits Oscilloscope Lab
Physics 222 RC Circuits Oscilloscope Lab
(Eq. 1)
(Eq. 2)
During the discharging phase (Fig. 1B), the voltage across the capacitor (Vc) and the voltage across the resistor
(Vr) are described by:
Voltage across capacitor during discharging phase =
(Eq. 3)
(Eq. 4)
The half-time,
, is the time required for each circuit element to reach the midpoint between its initial and final
Figure 1A
Figure 1B
You will use the oscilloscope to examine these time-dependant voltages. The square wave output from the signal
generator will charge and discharge the capacitor multiple times each second. The capacitor charges when the
square wave is in the high potential state and discharges when the square wave is in the low potential state.
Because the square wave signal acts both as the emf source and the switch, no physical changes in the circuit are
required. You will use analyze the voltage vs. time curves displayed on the oscilloscope to determine half-times
of RC circuits. This will measure the capacitance of commercial capacitors as well as a home-made pyrex
beaker/salt water system. The capacitance of the beaker system can be approximated as
where
A is the effective area (including circular side plus flat bottom, height = height of water) of the beaker, D is the
thickness of the beaker glass, and is the dielectric constant of pyrex ( =5).
Procedure
1) Using the signal generator, a known resistor, an unknown capacitor, configure a circuit having the same
characteristics as those shown in Figs. 1A-B. Make sure that the capacitor is connected to the Earth ground
portion of the circuit. Configure channel 1 of the scope to measure the output voltage from the signal generator.
Configure channel 2 of the scope to measure the voltage across the capacitor. Make sure that the grounds of both
channels of the scope are connected to the ground of the signal generator.
2) Record the value of your resistor in the first empty row of Table 1 below.
3) Measure the half-time from the oscilloscope screen and record your values in Table 1. Measure the half-time
during both the charging and discharging phases (commercial capacitors). Compute the average measured halftime (Record in Table 1) and use it to compute the measured capacitance (See Eq. 5). Compare measured and
expected values of capacitance and compute the % difference. Repeat steps 2-3 using a different capacitor (and
possibly a different resistor). The 3rd trial will involve the pyrex beaker capacitor (discharging phase).
Table 1: Data for RC Circuit Experiment (Part One)
R
Measured
Measured
Average
Measured
Expected
% diff
half-time
half-time
measured
capacitance
capacitance
()
charging
discharging
half-time
(F)
(F)
across C
across C
(s)
(s)
(s)
4) The pyrex beaker capacitor is constructed of the inner pyrex beaker, the outer pyrex beaker and salt water in
both beakers. Fill the inner beaker to the 500 ml level with salt water. A small amount of salt water is placed in
the outer beaker such that when the inner beaker is placed inside the outer beaker, the water level slightly exceeds
the 500 ml level of the inner beaker. Construct an RC circuit using the beaker capacitor and a resistor with a
large resistance (order of 105 ohms to reduce the relative uncertainty of the resistance). Use paper clips as
electrodes. Measure the resistance of the resistor/salt water conducting path using the multi-meter and record in
the table above. Do this by placing both electrodes into the salt water of the inner beaker. Then, remove one of
the electrodes and position it the salt water outside of the beaker. Measure the dimensions of the inner beaker
using the vernier caliper and record below. Use the half-time method to measure the capacitance of the pyrex
beaker capacitor but only consider the discharging phase.
inner diameter (m) = _____________________
Questions
1) What is the maximum charge that can be stored in an RC circuit with R=100.0 k, C=10.0 F and an applied
voltage of 4.00 Volts?
2) How much time does the same RC circuit require to become fully charged assuming that the capacitor was
initially uncharged?
3) How long does it take for the same RC circuit to accumulate 63% of its maximum charge?
4) How many RC time constants does it take for the same RC circuit to accumulate 99% of its maximum charge?
Your result should include 3 significant figures.
5) Assuming that the same RC circuit is fully charged and then suddenly shorted out, how much time does it
require to completely discharge?
6) How long does it take to discharge the same RC circuit to 37% of its initial charge?
7) How many RC time constants does it take for the same RC circuit to loose 99% of its initial charge? Your
result should include 3 significant figures.