Experiment 7 Voltage, Current, Resistance and Capacity
Equipment. 850 interface, Computer, Voltage Sensor, Current Sensor, 1 kΩ resistor, 3 kW resistor,
2.2 µF Capacitor, 0.47 µF Capacitor, Multimeter.
1. Purpose
To investigate how voltage and current behave in resistors and capacitors.
2. Introduction
C
Vo
R
VR
I
Figure (1) A voltage Vo is applied across a capacitor C and resistor R connected in series. This
causes a transient current I around the circuit, and a transient voltage VR across the resistor.
Figure (2a) The voltage V0 is applied at time t = 0
Figure (2b) The voltage VC (t) across the capacitor, as a
function of time t. The VC (t) increases as the capacitor
charges up to a voltage V0
Figure 2(c) The voltage VR across the resistor as a function of time tt.
VR (t), and the current I(t), fall to zero as the capacitor charges up.
If the voltage V0 is applied suddenly to the circuit of Fig. (1), then the subsequent behaviour is
described in Fig. (2). The current I(t) and the voltages VC (t), VC (t) and the capacitor charge q(t) obey the
equations
V0 = VC + VR
(1a)
VC = q C
(1b)
VR = IR
(1c)
I = dq dt
(1d)
This set of equations has a solution
VR = V0 [exp(- t t )]
(2a)
VC = V0 [1 - exp(- t t )]
(2b)
I = (V0 R )[exp(- t t )]
(2c)
where the time constant t is given by
t = RC
(2d)
Fig. (2) displays the Equ.s (2a) and (2b).
3. Experiment
The circuit of Fig. (1) is implemented in the laboratory by setting up Fig. (3). This differs from Fig.
(1) in a number of important respects.
C /F
Interface
850
Signal
Generator
Output
Current Sensor
On 850 intf
Channel B
R /W
Voltage Sensor
On 850 intf
Channel A
Vo
Io
Figure (3) The 850 Interface Signal Generator is used as a voltage source. The PASCO voltage
sensor and current sensor are used to measure the current round the circuit, and the voltage across the
resistor
First, all voltage sensors, and voltmeters, require an input current to make them work; they take some
energy from the circuit to which they are attached, and thus change the circuit. This is best characterised by
recognising that a voltmeter has an input resistance RVolt. An ideal voltmeter, which does not exist, has RVolt =
¥; it’s attachment between two points on a circuit has no effect on the circuit. The PASCO voltage sensor has
an input resistance greater than 1MW. We will use values of R in the range 1 to 10 kW. Thus, the attaching of
the voltage sensor produces less than a 1% change of the resistance in series with the capacity C. Thus we will
neglect the effect.
Second, all current sensors, and ammeters, have a resistance, RAmp . The ideal ammeter, which does
not exist, has RAmp = 0; it’s presence in the circuit would have no effect on the circuit. The PASCO current
sensor has a resistance of 1 W. Thus, it’s presence leads to less than a 0.1% change of the resistance in series
with the capacity C. Thus we will neglect the effect.
Third, all voltage sources have an output resistance, ROut , which appears in series with the output. An
ideal voltage source has ROut = 0; then, no matter how much current is taken from the source, its voltage does
not change. The PASCO Signal Generator has an ROut less than 1 W. Thus its effect also can be neglected.
Thus, Fig. (3) is a very close copy of Fig. (1), for the measuring instruments, and the voltage source
properties, produce less than a 1% change of the circuit parameters. However, there is now the advantage that
the currents and voltages at all places can be measured. Thus the experiment is able to verify that the circuit of
Fig. (1) is correctly analysed by the Equs (2).
4 Procedure
4.1 Now that your circuit is set up:
o
o
o
o
Programme the Signal Generator to give an output square wave, of amplitude 5 volts, and
frequency 100 Hz, with a sampling rate of at least 5 kHz. These values are then adjusted so
that the best signal is produced on an oscilloscope screen.
Programme the Signal Generator so measurements of Output Voltage and Current can be
made. Use the Signal Generator in AUTO Mode. It then turns on and off as RECORD and
STOP are used.
Set up an Oscilloscope Display Window, and use it to show the Output Voltage.
Use START and STOP to run the Signal Generator, and attempt to display the Output
Voltage on the Graph. You need display only a few periods of the wave, taking a few
milliseconds. This step must be completed, with play and practise, with confidence, with
demonstrator assistance, before proceeding further.
4.2 Data displays:
Use the Display of the Output Voltage to check that the amplitude, shape, frequency and sample rate
seen on the graph are those programmed into the generator.
4.3 Set up the circuit of Fig. (3).
o
Programme the Signal Generator so additionally measurements of Output Current can also
be made. Display the
(i) Output Current,
(ii) Circuit Current,
(iii) Voltage across R
(iv) Output Voltage
as Scope displays. Arrange that these 4 graphs can be simultaneously be displayed, with the same
time axis scale.
4.4 It is necessary, for a good display, to have the period, T, of the square wave greater than the time
constant t., of the circuit. Then, each step change of the input voltage occurs at a time such that the
effects of the previous step have decayed exponentially to zero. Then, each step should lead to
currents and voltages evolving in time as equations (2). You can vary T by changing the frequency of
the square wave.
4.5 When you have a good display, save it, for subsequent printing for use in your report.
4.6 Determine an experimental value for t from your display as follows:
Choose a part of your display that contains the decaying exponential of Equ. (2a) or Equ.(2c). A
property of an exponential decay is that in a duration of time of length t the value at the end of the
duration falls to 1/e = 36% of the value at the start of the duration. This can be used to determine t.
Use the ‘cursor’ function to locate your V, t co-ordinates.
Alternatively, an exponential fit to a selected part of a decay, using the “fit” feature of “graph
display”, can be used.
In either case, a single decay, well displayed, should be used, to obtain an accurate value for t.
4.6 Use the multimeter to measure the resistance R, read off the capacitor its capacitance C, compute
a theoretical value for t, and compare it to your experimental value.
4.7 The 2 values of R and C supplied allow of 4 RC combinations. Compare your experimental and
theoretical values of t for each of these combinations. A table will be a good way of presenting your
conclusions, including errors (uncertainties).
5. Exhortation This experiment is an ideal chance to try and obtain a physical understanding of
difficult ideas. You are exhorted to use the demonstrator, and to attempt to understand all the phenomena that
are present in your graphs of currents and voltages against time.
6. Finally Finishing Up. Please leave the bench as you found it. Thank you
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