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ECE 2000 – Spring 2004
Lab Experiment
Capacitors
Objective: To determine the basic characteristics of capacitors.
Prelab:
Read the handouts on capacitors.
For the circuit in Fig. 1, the current through the circuit and the voltage across the capacitor are given by
where RCiscalledthe"timeconstant"ofthe circuit.
V() ( 1 )for 0,
() for 0, and
c
=
−
−
τ
τ
t V e t
e t R
V
it
t s
s t
Using Matlab, plot i(t) and Vc(t) for t = 0 to t = 5 on a single graph. Provide a suitable title, labels for the x
and y-axes, a grid, and a legend for the two functions.
Lab Procedure:
CAUTION: In part of this experiment, you will use electrolytic capacitors which are polarized, i.e., they
have positive and negative polarity markings. They can be used only in DC circuits or DC with small
superimposed ac voltages. They must be connected using the correct polarity. A wrong polarity connection
may cause an explosion and accident. If you are not sure, have your circuit checked before you power the
circuit.
In this experiment, record readings and waveforms on a separate paper. At the end, have the paper
signed by the TA. The waveforms should be recorded by each student separately.
Step 0.
Select a capacitor from your lab kit and measure the resistance of it using the DMM. The resistance
(to a DC current) of the capacitor is ____________________________.
Step 1.
Select the resistor and capacitor to be used for the circuit in Fig. 1. Determine the time constant as the
product of R and C, which is ______________________.
Set up the circuit shown in Fig. 1. Using an alligator lead, short the capacitor.
Adjust the DC supply voltage to 20 V. Record the initial current reading on the multimeter: ___________.
When you open the alligator lead, current flows through the capacitor. As current goes through the
capacitor, charges accumulate in the capacitor and the voltage across the capacitor increases and
consequently the current through the circuit decreases. In about five times the time constant, the capacitor
is charged to the supply voltage and the current becomes nearly zero.
You will now record this decay of the current. You will take the readings at ∆ t = τ/ 5 intervals. So in a
table, note down the time instances at which the readings will be taken. Now get ready for some serious
data taking. You will need a watch.
Record the initial current. At reference time t = 0, open the alligator lead. Take the current reading for
every ∆ t until the current is negligibly small.
Now discharge the capacitor by shorting it briefly using the alligator clip. Repeat the experiment a
second time and measure the current values at the same time instants as the first trial.
For each time instant calculate the average current values from the two sets of readings then calculate
the voltage across the capacitor as Vc = Vs - i R.
Plot on graph paper the voltage across the capacitor Vc in the y-axis and time in the x-axis. You will
notice that this is an exponentially decreasing waveform. You must also plot the current i(t) on the same
graph. You will note that these waveforms are nearly identical to those obtained using Matlab.
From the voltage plot, measure the time for the voltage across the capacitor to rise to 63.2% (that is 1 1
− − e ) of the final value (which will be the supply voltage) from zero. You should find that this time
period is equal to the time constant calculated earlier.
Measured time constant = ____________
Calculated time constant = _____________
From the current plot, measure the time for the current to fall by 63.2% of the initial value. You should
find that this is also equal to the time constant.
Step 2.
Replace the DC power supply by a function generator and connect the oscilloscope as shown in Fig. 2.
The capacitor in this circuit must be non-polarized as the voltage is alternating between positive and
negative.
Adjust the function generator to give 5 square wave at 500 Hz. Observe the capacitor voltage.
Record the waveform on graph paper.
V (^) p − p
i
0 − 2 mA
R = 47 K
Vs = 20 V C = 100 μ F Vc
lead
alligator
Figure 1 :Chargingof a capacitor
Multimeter
Figure 2 :Capacitorcircuit excitedbyperiodic waves
oscilloscope
10 k Ω
- 1 μ F
Function Generator
