Download bme 211 circuit theory

EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
BAŞKENT UNIVERSITY
BIOMEDICAL ENGINEERING DEPARTMENT
BME 211 CIRCUIT THEORY-I LAB
EXPERIMENT I
MEASUREMENT OF VOLTAGE,CURRENT AND RESISTANCE
OBJECTIVE: Measurement of current, voltage and resistance quantities with a multimeter
and experimental verification of KVL and KCL.
1. INTRODUCTION
1.1 MULTIMETERS
Multimeter is an instrument for measuring basically the values of current,voltage and
resistance. It is possible to reach the correct measurement if the appropriate mode of
operation and range are selected. Otherwise either the meter can be damaged or the
measurement can be incorrect.
The symbolic representation of a multimeter is shown below in Fig.1. The output terminals
are denoted by the signs +(red cable) and –(black cable).
Fig. 1 Symbolic representation of a multimeter
1.2 MULTIMETER IN THE CURRENT MODE (AMPERMETER)
The basic operating principle of an ampermeter is to obtain a voltage across a shunt resistor
and compare this voltage with a reference level. In order to use the multimeter as an
ampermeter, one has to observe the following directions:




The switches on the meter should be selected correctly. (A button for current)
There are usually two divisions for current measurements: one for small currents and
one for large currents. You should work with the big scale if the current you are
trying to measure can be bigger than the value of the small scale.
DC/AC selection should be performed. We will be working with DC signals in our
experiments. In DC (Direct Current) circuits, the meter is to be connected in such a
way that the current enters the instrument from the (+) terminal. Otherwise the pointer
will deflect in the reverse direction(in analog meters) or the reading will be negative.
The meter should be connected in series to any network. Ampermeters have a very
small internal resistance; in fact it is supposed to be zero.
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EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
As an example, refer to Fig. 2. If one wants to measure the current I1 in R1 then all the
switches must be properly set, so that the meter acts as an ampermeter. The meter terminals
are connected to the branch in series; the same current with the device should be passed
through our meter.
R1
R3
R1
R2
V1
R4
R3
R2
A
V1
R4
Fig. 2 Current measurement
Other current values can be obtained similarly.
1.3 MULTIMETER IN THE VOLTAGE MODE
The basic operating principle is to compare the unknown voltage with a reference level. As in
the ampermeter case one has to set the switches on the meter properly, so that the meter acts
as a voltmeter. Pay attention to the following:



The switches on the meter should be selected correctly. (V button for voltage)
DC/AC selection should be performed as DC. In AC (Alternating Current) circuits, the
connection of the terminal polarities are not important. But for DC measurements one
has to pay attention to the connections. Other wise an opposite (positive-negative)
reading may result.
The meter should be connected in parallel to any network. Voltmeters have a very
large internal resistance; in fact it is supposed to be infinite. Why?
As an example, refer to Fig. 3. If one wants to measure the voltage V3 across R3 then the
meter should be connected as follows:
V
R1
V1
R3
R2
R1
R4
V1
R3
R2
Fig. 3 Voltage measurement
2
R4
EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
1.4 MULTIMETER IN THE RESISTANCE MODE
The basic principle is to apply a test current of known value to the unknown resistor and
compare it with the voltage that is obtained across a known resistor. The meter is again
connected in parallel to the device. It is recommended that you choose the biggest scale, read
the value and then decrease the scale for sensitive reading. The following section is about the
color coding of resistors.
1.5 RESISTOR COLOR CODING
The most widely used resistors are of carbon type. There exists usually four color bands on
the body; indicating the ohmic values and tolerances. In order to achieve a correct reading,
one has to hold the resistor in such a way that the bands are close to the left hand side. Then
the ohmic value is given by :
R  AB*10 C  %D OHMS
that is ; simply put A and B values together to form a two-digit number and multiply it with
10 C .
A B C D
COLOR
Black
VALUE
0
TOLERANCE
-
Brown
1
-
Red
2
-
Orange
3
-
Yellow
4
-
Green
5
-
Blue
6
-
Violet
7
-
Gray
8
-
White
9
-
Gold
-1(for C only)
%5
Silver
-2(for C only)
%10
No Color
-
%20
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EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
Examples:
*1 A=green
B=blue
C=red
D=gold
then the value is: 56x102  %5 that is 5.6 kOHMs
*2 330k  %10 is given find the colors:
3 → orange
3 → orange
33x104 : 4 → yellow
%10 → silver
2. PRELIMINARY WORK
2.1 Calculate the values of the currents I1, I2, I3, I4 and the voltages V1, V2, V3, V4, in Fig. 4
Show the meter connections for these measurements.
I3
I1
I2
I4
Fig. 4
2.2
For the circuit given in Fig.5, one resistor’s value isn’t known. But we know resistor R
dissipates 2W. With these parameters find the value of R.
6 ohm
R
3 ohm
Fig.5
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EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
2.3 Find the equivalent resistance Rab between the points a and b for the circuit in Fig. 6.
a
5k
1k
1k
1k
6k
Rab=?
2k
12k
2k
1k
Fig. 6
b
5k
1k
0
2.4 Find the equivalent resistance Rab between the points a and b for the circuit in Fig. 7.
4k ohm
4k ohm
4k ohm
4k ohm
4k ohm
Fig. 7
2.5 For the circuit shown in Fig. 7, the value of R2 is required to be measured. Why doesn’t
such a connection give the correct value? Redraw the circuit showing the true connections.
R
R1
V1
R2
Fig. 8
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EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
2.6 For each of the resistance values given, write down the correct color bands.
a) 100  %10
b) 120k  %5
c) 22  % 5
d) 3.3  % 5
2.7 Find the values of the resistors for which the following color bands are given.
a) red-black-red-silver
b) red-red-gold-gold
c) green-blue-gold-no color
d) violet-gray-gold-no color e) red-white-orange-no color
3. EXPERIMENTAL WORK
3.1 Measure the values of each resistor given to you.
3.2 Setup your preliminary circuit.
I3
I1
I2
I4
Fig. 7
3.3 Measure the values of currents I1, I2, I3, I4 and voltages V1 V2, V3, V4, and compare them
with your preliminary work values.
3.4 Disconnect the voltage source at points a and f and measure the value of Raf
3.5 What is the minimum value of resistor R, if we want maximum 10 mA over Lamp.
I
Calculate theoretical result of R then Setup the circuit above with the theoretical R
value and measure the current I.
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EXPERIMENT I
MEASUREMENT OF VOLTAGE, CURRENT AND RESISTANCE
Name
Lastname
Student id
Set No
4. RESULTS and CONCLUSION
:
:
:
:
4.1 Using the experimental results, try to prove KCL at nodes b and e.
4.2 This time try to prove KVL for the closed loops abefa, bcdeb and abcdefa.
4.3 Compare your theoretical Raf value with the measured one.
4.4 Give comments on the differences between your theoretical calculations and experimental
results.
5. REPORT: Please write your experimental results.
3.1)
3.3)
I1=
I2=
I3=
I4=
V1=
V2=
V3=
V4=
3.4)
Raf=
3.5)
Theoretical Calculations:
R=
Experimental result of I=
4.1)
4.2)
4.3)
4.4)
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