EXP.1-Basic 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(10-1) 5Silver - -2(10-2) 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 1a-2.

2. The maximum and minimum values for each resistor were calculated.

Results were recorded in Table 1a-2 accordingly.

3. By using digital multimeter, actual value of resistors were measured and

recorded in Table 1a-2. 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 1-2, 2-3 and 1-3 and the

measured values were recorded in Table 1a-3.

3. The values under 1-2 and 2-3 were added and the result was compared to

the 1-3 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 1a-3.

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 1a-2

1st Trial 2nd Trial 3rd TrialR1-2(Ω) 1.50k 4.49k 7.41kR2-3(Ω) 7.64k 4.66k 1.74kR1-3(Ω) 9.10k 9.11k 9.08k

R1-2 + R2-3(Ω) 9.14k 9.15k 9.15kTable 1a-3

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 1b-1.Then, the meter

was connected as shown.

7. The circuit was broken as shown in Figure 1b-2 and the other meter set

was inserted on mA current range.

8. The current flowing in the circuit was recorded in Table 1b-1.

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 1b-1 Figure 1b-2

Results:

Vsupply (volt) 2 4 6Current (mA) 0.972 1.947 2.924Theoretical values (mA)

1.0 2.0 3.0

Table 1b-1

Graph I-V

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 1c-1 was connected with R=5kΩ.

2. The actual value of the resistor was measured and then the result was

recorded in Table 1c-1.

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 1c-1.

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 1c-2.

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 1c-1

Slope (G) R (1/G)Table 1c-1 0.199 5.02

Theoretical Current Value 0.20 5

Table 1c-2

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 I-V (From Table 1c-1)

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 1d-1

Method :

1. Circuit is connected as figure 2-1a 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 1d-1 is filled up.

Parallel Circuits Diagram:

Figure 1d-2

Method:

1. Circuit is connected as figure 2-1b 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 1d-1

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 1d-3

Calculations:

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)1.814×10-3 1.013×10-3 0.668×10-3 0.148×10-3 1.829×10-3

Table 2-2

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 1d-4

Calculations:

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 cross-sectional 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.

EXP.1-Basic Ohm's Law

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