EXP.1Basic Ohm's Law

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Transcript of EXP.1Basic Ohm's Law
TEST (a): RESISTOR COLOR CODE
Aims:
o To determine the value of resistors according to the Electronic Industries Association (EIA) color code and through measurement.
o To investigate the properties of potentiometer.
Apparatus:
Digital Multimeter – FLUKE 73 III MULTIMETER (Current range: 200mA) Resistors: R1=150 Ω, R2=20k Ω, R3=5.1MΩ Linear 10kΩ potentiometer
Reference Table:
Color Significant figure(1st and 2nd band)
Number of zeros(multiplier)(third
band)
%Tolerance
(Forth Band)
Black 0 0(100) Brown 1 1(101) 
Red 2 2(102) Orange 3 3(103) Yellow 4 4(104) Green 5 5(105) Blue 6 6(106) 
Violet 7 7(107) Gray 8 8(108) White 9 9(109) Gold  1(101) 5Silver  2(102) 10
No color   20
Resistor color code
Method:
Resistor Color Code:
1. Five different values of resistors were taken to be determined using color
code table. Each resistors nominal value and tolerance was defined and
recorded in Table 1a2.
2. The maximum and minimum values for each resistor were calculated.
Results were recorded in Table 1a2 accordingly.
3. By using digital multimeter, actual value of resistors were measured and
recorded in Table 1a2. The values were checked whether or not fall
between the calculated ranges in step 2.
Variable Resistor:
1. The end terminals and wiper terminal for the potentiometer were
determined. The terminals were labeled and numbered 1,2 and 3 being the
wiper respectively.
2. The ohmmeter was positioned across terminals 12, 23 and 13 and the
measured values were recorded in Table 1a3.
3. The values under 12 and 23 were added and the result was compared to
the 13 value (theoretical value).
4. The shaft of the potentiometer was reposition and the procedures for steps
2 and 3 were repeated for another 4 trials. The results was recorded in
Table 1a3.
TABLES OF RESULTS
Test (a): Resistor Color Code
Resistors R1 R2 R3
Nominal Value (Ω)
150.0 20.0k 5.10M
Tolerance (%) 5 5 5Maximum Value(Ω)
149.5 19.67k 5.08M
Minimum Value(Ω)
149.2 19.66k 5.05M
Measured Value(Ω)
149.3 19.67k 5.07M
Table 1a2
1st Trial 2nd Trial 3rd TrialR12(Ω) 1.50k 4.49k 7.41kR23(Ω) 7.64k 4.66k 1.74kR13(Ω) 9.10k 9.11k 9.08k
R12 + R23(Ω) 9.14k 9.15k 9.15kTable 1a3
Calculations:
A .Resistor Color Code:
i ) Maximum and minimum value:
1. 0.05 × 150 Ω = 7.5 Ω Maximum value = 157.5 Ω Minimum value = 142.5 Ω
2. 0.05 × 20k Ω = 1k Ω Maximum value = 21k Ω Minimum value = 19k Ω
3. 0.05 × 5.1M kΩ = 255 kΩ Maximum value = 5.355 MΩ Minimum value = 4.845MΩ
ii ) The percentage of relative error:
% of relative error = (theoretical value – experimental value ) × 100 % theoretical value
1. ( 150 Ω  149.3 Ω ) × 100 % = 0.47 %150Ω
2. ( 20k Ω  19.67k Ω ) ×100 % = 1.65 %20kΩ
3. ( 5.1MΩ  5.07MΩ ) × 100 % = 0.59 %5.1 MΩ
B. Variable Resistor:
The percentage of relative error:
1. ( 9.14k Ω  9.10k Ω ) × 100 % = 0.44 % 9.14kΩ
2. ( 9.15k Ω  9.11k Ω ) × 100 % = 0.44 % 9.15kΩ
3. ( 9.15k Ω  9.08k Ω ) × 100 % = 0.77 % 9.15kΩ
TEST (b): VOLTAGE & CURRENT MEASUREMENTS
Aims:
o To measure voltage and current in DC circuit.
Apparatus:
2 Digital Multimeter – FLUKE 73 III MULTIMETER (Current range: 200mA) DC voltage supply 2 kΩ resistor
Method:
1. The power supply was switch on and was adjusted for the minimum
output.
2. The digital multimeter was set to measure voltage.
3. The voltmeter was connected directly to the power supply terminals.
4. The effect of turning the output voltage control was observed.
5. The voltage was adjusted to 2 volts.
6. The meter was remove and the 2 kΩ resistor was connected across the
terminals of the power supply as shown in Figure 1b1.Then, the meter
was connected as shown.
7. The circuit was broken as shown in Figure 1b2 and the other meter set
was inserted on mA current range.
8. The current flowing in the circuit was recorded in Table 1b1.
9. The voltage was increased in 2 volt steps, and for each value of the
voltage, the current was recorded.
R1 2k
V 1V dc+

R1 2k V
+
V dc

A
+
V
Figure 1b1 Figure 1b2
Results:
Vsupply (volt) 2 4 6Current (mA) 0.972 1.947 2.924Theoretical values (mA)
1.0 2.0 3.0
Table 1b1
Graph IV
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8
Voltage,V
Cu
rren
t,I
Calculations:
The percentage of relative error:
1. 0.972 – 1.0 × 100 % = 2.8 % 1.0
2. 1.947 – 2.0 × 100 % = 2.7 % 2.0
3. 2.924 – 3.0 × 100 % = 2.5 % 3.0
TEST (c): OHM’S LAW
Aim: o To verify Ohm’s Law.
Apparatus:
Voltage DC supply Resistors – 5.1kΩ Two digital DMMs.
Method:
1. The circuit in Figure 1c1 was connected with R=5kΩ.
2. The actual value of the resistor was measured and then the result was
recorded in Table 1c1.
3. The voltage across R was increased in 1V steps until 9V, and for each case
the resulting current was measured and recorded in Table 1c1.
4. The graphs of I versus V was plotted for both table of results on the same
scales and axis.
5. A right triangle was constructed on each graph, and from this. The slope
was determined again and hence the conductance G was evaluated.
6. From this information, the resistance R was evaluated. G and R for each
graph were recorded in the appropriate column in Table 1c2.
7. This obtained value was compared experimentally with those measured
values recorded in the respective tables.
Results:
Nominal Resistance R=5.1kΩ
Measured ResistanceR= 5.03 kΩ
Voltage Source
Vs(V) 0 1 2 3 4 5 6
Current (mA) 0.017 0.200 0.399 0.599 0.793 0.999 1.195Theoretical
Current Values
(mA) 0 0.200 0.400 0.600 0.800 1.000 1.200
Table 1c1
Slope (G) R (1/G)Table 1c1 0.199 5.02
Theoretical Current Value 0.20 5
Table 1c2
Calculations:
The percentage of relative error (examples of calculations):
1. 0.200 – 0.200 × 100 % = 0.00 % 0.200
6. 1.200– 1.195 × 100 % = 0.42 % 1.200
Graph IV (From Table 1c1)
0, 0.017
1, 0.206
2, 0.399
3, 0.599
4, 0.798
5, 0.999
6, 1.195
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7Voltage (V)
Curr
ent,
I (m
A)
TEST (d): SERIES AND PARALLEL CIRCUITS
Aims:
o To verify that in series circuit;
i) The total resistance is equal to the sum of the individual resistors
ii) The voltage drops across the resistors equals to the applied voltage
iii) The value of the current is the same in all parts of the circuits.
o To verify that in parallel circuit;
i) The equivalent resistance is the reciprocal of the sum of reciprocal of
the individual resistors.
ii) The branch current equal to the supplied current
iii) The voltage across each resistor is the same.
Apparatus:
15V dc supply.
2 digital multimeters.
Resistors; 1.0kΩ, 1.5kΩ, 6.8kΩ.
Series Circuit Diagram:
Figure 1d1
Method :
1. Circuit is connected as figure 21a and supply voltage is adjusted to 15 V.
2. The power supply is switched off and then ammeter is connected in position
A.
3. The power supply is switched off. The current via resistor, R1 is read.
4. The voltmeter across R1 is connected and the voltage drop across it is
measured.
5. Method 2 until 4 is repeated for the ammeter positions B, C and D and the
voltmeter positions R2 and R3.
6. The voltage for close and opened loop is recorded. The measured values in
table 1d1 is filled up.
Parallel Circuits Diagram:
Figure 1d2
Method:
1. Circuit is connected as figure 21b and supply voltage is adjusted to 15 V.
2. The power supply is switched off and then ammeter is connected in
position A, the total current, Itotal. The supply is switched on the current
through resistor, R1 and its voltage drop across it is read.
3. Method 2 is repeated for the ammeter positions B, C and D and the
voltmeter positions across R2 and R3.
Caution: Be careful not to touch R3 during measurement as it might be hot.
Tabulated Results (series circuit):
Supply voltage (volt)
V1 (volts) V2 (volts) V3 (volts) voltage sum V1+ V2+ V3
12 1.31 1.96 8.9 12.17
Supply current (mA)
I1 (mA) I2 (mA) I3 (mA) Total current (mA)
1.29 1.3 1.3 1.3 1.3
Total resistance (Ohms)
R1
(Ohms)R2
(Ohms)R3
(Ohms)Resistance sum
R1+R2+R3
9.3k 1.001k 1.490k 6.77k 9.261k
Table 1d1
Calculated values:
Voltage drop over resistorSupply voltage
(V)
Total current
(A)
I1 I2 I3 R1
(Volts)R2
(Volts)R3
(Volts)
12 1.3 1.3 1.3 1.3
Equivalent Resistance (Ω)
9.300k
Table 1d3
Calculations:
% of relative error =  theoretical value – experimental value  × 100 % Theoretical value
The percentage of relative error (voltage drop):
1. For R1  1.61 V  1.599 V  × 100 % = 0.68 % 1.61 V
2. For R2  2.415 V  2.421 V  × 100 % = 0.25 % 2.415 V
3. For R3  10.948 V – 10.91 V  × 100 % = 0.35 % 10.948V
The percentage of relative error (current):
4. For I1  1.3 mA – 1.3 mA  × 100 % = 0% 1.29 mA
5. For I2  1.3 mA – 1.3 mA  × 100 % = 0% 1.29 mA
6. For I3  1.3 mA – 1.3 mA  × 100 % = 0% 1.29 mA
The percentage of relative error (total current):
7. For Itotal  1.3mA  1.3mA  × 100 % = 0%1.29mA
The percentage of relative error (equivalent resistance):
8. Equivalent Resistance:  9.300kΩ  9.261kΩ  × 100 % = 0.43 %
9.300kΩ
Tabulated Results (parallel circuit):
Measured Value:
Supply current (Ampere)
I1 (mA) I2 (mA) I3 (mA) ∑ Current
21.6 12.5 6.29 2.84 21.63
Supply voltage (Volt)
V1 (Volt) V2 (Volt) V3 (Volt)
12 12.3 12.3 12.3 12.3
Equivalent resistance(kΩ)
R1 (kΩ) R2 (kΩ) R3 (kΩ) Equivalent resistance (kΩ)
0.529 0.965 1.52 5.72 0.525
Total conductance
G1
(Siemens)G2
(Siemens)G3
(Siemens)Conductance
sum G1+G2+G3
(Siemens)1.814×103 1.013×103 0.668×103 0.148×103 1.829×103
Table 22
Theoretical values:
Voltage drop over resistor Supply voltage
)V(
Total current( mA)
I1 I2 I3 R1
(volts)R2
(volts)R3
(volts)
12.00 21.6 12.5 6.30 2.8 12.00 12.00 12.00
EquivalentResistance
0.529 ΩTable 1d4
Calculations:
% of relative error =  theoretical value – experimental value  × 100 % Theoretical value
The percentage of relative error (voltage drop):
1. For R1  12.00 V – 12.3 V  × 100 % = 0.25 % 12.00 V
2. For R2  12.00 V – 12.3 V  × 100 % = 0.25% 12.00 V
3. For R3  12.00 V – 12.3 V  × 100 % = 0.25 % 12.00 V
The percentage of relative error (current):
4. For I1  12.50 mA – 12.50 mA  × 100 % = 0% 12.50 mA
5. For I2  6.30mA – 6.30 mA  × 100 % = 0 % 6.30 mA
6. For I3  2.8 mA – 2.84 mA  × 100 % = 0.14 % 2.8 mA
The percentage of relative error (total current):
7. For Itotal  21.6mA  21.63 mA  × 100 % = 0.13 %21.6 mA
The percentage of relative error (equivalent resistance):
8. Equivalent Resistance:  529 Ω  525 Ω  × 100 % = 0.75%
529 Ω
DISCUSSION
1. The value of resistance can be determined by reading the 4 color bands according to the Resistor Color Code.
2. Percentage error is calculated by using the formula below:
% of relative error = Theoretical value – experimental value  × 100 % Theoretical value
3. For test (a), percentage difference for resistor 150Ω is 0.47% and for 20kΩ is 1.65% while 5.1MΩ is 0.59%. The error for all resistors is small and their value is approximate to the nominal value.
4. For variable resistor in test (a), the percentage error calculated for the first trial is about 0.44%, second trial gave us 0.44% of error and the third trial gave 0.77% of error.
5. For test (b), voltage is calculated by using voltmeter and the ammeter must be connected parallel to the circuit.
6. Current is calculated by using ammeter and the while ammeter must be connected series to the circuit.
7. For Test (c), The Ohm’s Law has been verified from the graph that the voltage, V across a resistor is directly proportional to the current, I, flowing via the resistor.
V= IR
8. The fact that supporting our decisions is the voltage measured across and the current through known resistors for several different values. Then, the data were plotted on a graph and yielded a straight line, proving that the relationship between voltage and current is linear.
9. The factors that affect resistance of a material with a uniform crosssectional area are resistivity (ρ) and length of the resistance material.
10. Two types of common resistors are wire wound and composition type. Wire wound resistors are normal types of resistor while composition resistors used when large resistance is needed.
11. Not all resistors obeying Ohm’s Law, only linear resistors obey Ohm’s Law. Nonlinear resistors such as light bulb and diode did not obey Ohm’s law because their resistance varies with current.
12. For Test (d), in series circuit, the total resistance is equal to the sum of the individual resistors. Mathematically;
Rtotal= R1+R2+R3.
13. In a parallel circuit, the equivalent resistance is the reciprocal of the sum of reciprocals of individual resistors. Mathematically;
1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3
14. In series circuit, the voltage drops across resistors equals to the applied voltage. Mathematically;
Vtotal= V1+V2+V3
15. In parallel circuit, the voltage drop across each resistor in parallel is the same. Mathematically;
Vtotal= V1 =V2 =V3
16. In series circuit, the value of current is the same in all parts of the circuit. Mathematically;
Itotal= I1 = I2 =I3
17. In parallel circuit, the branch current in parallel equal to the supply current. Mathematically;
Itotal= I1 +I2 +I3
18. The aim of the experiment had been achieved.
19. From the experiment we can see that the current is same throughout the series circuit, whereas in the parallel circuit the voltage is the same.
20. Error in circuit connection, error by ammeter and voltmeter and error in reading the current and voltage may contribute to the discrepancies in the results for each point of the aim
21. The principle of voltage division applicable to the voltage in the series circuit whiles the principle of current division applicable to the current in the parallel circuit.
CONCLUSION
1. Theoretically, the resistance value can be verified by referring to the resistor
color code while the measured resistance can be determined by using digital
multimeter.
2. The voltage is measured in parallel and current in this circuit is measured in
series.
3. The experiment has satisfied to Ohm’s Law that there is direct relationship
between voltage, V, and current, I , across resistor. The verified Ohm’s Law
represents the straight linear line of a graph Voltage, V vs. current, I, while its
slope represents the resistance.
4. In the series circuit, the total resistance is equal to the sum of the individual
resistors. The voltage drops across the resistors equals to the applied voltage.
The value of the current is the same in all parts of the circuits.
5. In the parallel circuits, the equivalent resistance is the reciprocal of the sum of
reciprocal of the individual resistors. The branch current in parallel equal to
the supply current. The voltage drop across each resistor in parallel is the
same.
6. There are few factors that affect the outcome of the results. Firstly, there might
be problems in the process of manufacturing the apparatus. Secondly, the
condition of the apparatus is poor as it has been used for a number of times
and get a little bit rusty. The voltage values could not be set exactly as the
required values due to human weakness. There is also resistance in the
apparatus used such as the wires and the digital multimeters.
7. Overall, the objectives of the experiment have been successfully achieved.