# Test Equipment Basic Dc Measurements And Ohms Law Biology Essay

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In a direct current circuit, there is only one direction of current flow within the circuit from the positive terminal of voltage to the negative terminal of voltage. In a circuit, the voltage source is being measured using a multimeter which has both analog (AVO) and digital (DMM) function. Voltmeter is always connected in parallel with the circuit or elements of which the voltage is to be measured. As for current source, it is being measured with an ammeter. This ammeter is also included in the same multimeter as the multimeter used to measure voltage which can be either analog or digital.

In a DC circuit, the value of voltage, current or resistance can be determined by applying Ohm's Law if the other two values are known or given within the circuit. Basically, Ohm's Law states that the current through the electric circuit is dependent on the resistance of the path and is given by:

V

R

which I is referred to electric current (A),

V is the potential difference between two points (V),

and R is resistance value (Î©).

From the Ohm's Law, the interrelationship between the current, voltage and resistance can be known. Therefore, in order to solve a simple circuit, Ohm's Law can be applied to find all the unknown values either for current, resistance and voltage.

Apart from Ohm's Law, Kirchoff's Laws can also be used in a to solve a simple circuit but a closed circuit is a must since Kirchoff's Laws can only be used in a closed circuit in order to determine the values of current, voltage and resistance. There are two types of Kirchoff's Laws, which are Kirchoff's Current Law and Kirchoff's Voltage Law. These laws are essential in circuit analysis tasks on solving more complicated circuit problems. Kirchoff's Current Law states that the sum of currents entering any junction must be equal to the sum of the currents leaving that junction which is denoted as

## :

Ientering = Ileaving

or

I = 0

As for Kirchoff's Voltage Law, it is algebraic sum of the changes in potential across all of the elements around any closed circuit lop must be zero. It can be denoted as:

Vdrop or rise = 0

For further analysis of problem solving on circuits, Voltage Divider Rule and Current Divider Rule can be considerable. The difference between these two rules is that Voltage Divider Rule can only be applied in a series circuit while Current Divider Rule applied in a parallel circuit. All of these rules Ohm's Law, Kirchoff's Laws and voltage and current divider rule can be applied together to solve any of the circuit problems.

## 2.0 Objective

The objective of this experiment is to introduce the different types of test equipments and the way to operate them. The various test instruments are as follows:

ï‚· Dual DC Power Supply

ï‚· Digital Multimeter

ï‚· Bread Board

## 3.0 Apparatus

The apparatus used in this experiment include:

Dual DC Power Supply: GPC-3030

Digital Multimeter: Fluke 175

Resistors: 1 x 470ï-, 1 x 820ï-, 1 x 1.8kï-, 1 x 8.2Mï-, 1 x 4.7Mï-.

Bread Board

## 4.0 Procedure

## 4.1 Use of DC Power Supply and Multimeter

The voltmeter was connected in parallel (across) the element being measured when measuring voltage levels, as shown in Fig. 1.1(a). If the leads were connected as shown in the figure, the reading would be up up-scale and positive; if the meter was hooked up in the reverse manner, the reading would be down-scale and negative. This proves that the voltmeter is an excellent instrument for measuring the voltage level and also for determining the polarity.

As for ammeters, they were connected in series with the branch in which the current was being treasured, as shown in Fig. 1.1(b), requiring the branch to be opened and the meter to be inserted. Ammeters have polarity markings, indicating the manner in which they should be connected to obtain an up-scale reading. As illustrated in the figure, the reading of an ammeter would be up-scale and positive since the current I would establish a voltage drop across the meter. If the meter was hooked up in the reverse manner, the reading would be negative or down-scale.

## Figure 1.1

The mode selector on the DC power or each of the supply unit was set to independent. For each of the variable outputs (Master & Slave) on the DC power supply, a short circuit was placed across the output and the voltage control was adjusted to mid-range. Then, the current control was adjusted to 300 mA using the current limit control and the power supply ammeter. The process for the Slave output was repeated and the current controls were not to be re-adjusted for the rest of the laboratory.

Next, the short circuit was removed and the output of both the Master and Slave was measured as well as adjusted to 15 V using the digital multimeter. The digital multimeter (DMM) was set for DC voltage measurement. After that, the DMM was set for Ohms measurement and each of the resistors supplied was measured. The body resistance was not to be in parallel with the resistor being measured.

## 4.2 Ohms Law

The circuits were connected as shown in Fig. 1.2, using the correct values of resistance. The first circuit was connected to output "Master Output" and the output voltage was set to 2V. Using the digital multimeter, the current drawn from the supply was measured.

The above measurements for Output voltage steps were repeated of 2 V to a maximum voltage of 20 V. The voltage across and the current through a resistor could be used to determine its resistance using Ohm's Law. A graph of current I versus voltage V was plotted and the value of R was calculated from the slope of the graph to verify Ohm's Law. The resistance was calculated from the measured values.

## Figure 1.2

## 4.3 Basic Measurement I (voltage and current polarity)

The circuits were connected as shown in Fig. 1.3, using the correct values of resistance. The first circuit was connected to "Master Output" and the output voltage was adjusted to 15 V. Then, the voltages across the supply and across each of the resistor were measured using the digital multimeter, noting the polarity of the voltage across each element. The current drawn from the supply and current through each resistor was also measured using the digital multimeter.

## Figure 1.3

## 4.4 Basic Measurement II (Voltage Reference Point)

The circuits were connected as shown in Fig. 1.4, using the correct values of resistance. The first circuit was connected to output Master and the output voltage was adjusted to 15 V. Then, the voltages across R1, R2, R3, VA, VB, VC, VD, VAB, VBC, and VCD were measured using the digital multimeter, noting the polarity of the voltage across each element. Using the results from previous voltages measurements, the voltage VAB, VBC, and VCD was calculated and compared with the measured results. Next, the voltage VCA was measured using the multimeter, noting the polarity of the voltage across the element and the calculated voltage VCA was compared with the measured result.

## Figure 1.4

## 4.5 Basic Measurement III

The circuits were connected as shown in Fig. 1.5, using the correct values of resistance. The first circuit was connected to "Master Output" and the output voltage was adjusted to 15 V. Then, the input voltage to the circuit, voltage across each resistor and the current drawn from the supply was measured.

## Figure 1.5

## 5.0

## Data & Results

## 5.1

## Theoretical &Experimental results of Ohm's Law

## Supply E1,V

## Measured Current, A

## Calculated Current, A

## Resistance, â„¦

0.0V

0.00

0.00

0.00

2.0V

4.11 x 10-3

4.26 x 10-3

486.62

4.0V

8.57 x 10-3

8.51 x 10-3

466.62

6.0V

13.15 x 10-3

12.8 x 10-3

454.55

8.0V

17.19 x 10-3

17.0 x 10-3

465.12

10.0V

21.82 x 10-3

21.3 x 10-3

458.72

12.0V

25.86 x 10-3

25.5 x 10-3

463.32

14.0V

30.09 x 10-3

29.8 x 10-3

466.67

16.0V

34.95 x 10-3

34.0 x 10-3

457.14

18.0V

39.12 x 10-3

38.3 x 10-3

460.36

20.0V

43.65 x 10-3

42.6 x 10-3

457.67

Table 5.1a: Experimental results of current values across 470 ï- resistor

## Voltage, V

## Resistance, â„¦

## Current, A

## Theoretical

## Experimental

0.0V

470

0.00

2.0V

470

4.11 x 10-3

4.0V

470

8.57 x 10-3

6.0V

470

13.15 x 10-3

8.0V

470

17.19 x 10-3

10.0V

470

21.82 x 10-3

12.0V

470

25.86 x 10-3

14.0V

470

30.09 x 10-3

16.0V

470

34.95 x 10-3

18.0V

470

39.12 x 10-3

20.0V

470

43.65 x 10-3

Table 5.1b: Calculation for theoretical and experimental results of Table 5.1a for current.

## Voltage, V

## Experimental Current, A

## Resistance, â„¦

0.0V

0.00

## ï-

2.0V

4.11 x 10-3

## ï-

4.0V

8.57 x 10-3

466.74ï-

6.0V

13.15 x 10-3

456.27ï-

8.0V

17.19 x 10-3

465.39ï-

10.0V

21.82 x 10-3

458.30ï-

12.0V

25.86 x 10-3

464.04ï-

14.0V

30.09 x 10-3

465.27ï-

16.0V

34.95 x 10-3

457.80ï-

18.0V

39.12 x 10-3

460.12ï-

20.0V

43.65 x 10-3

458.19ï-

Table 5.1c: Calculation for theoretical and experimental results of Table 5.1a for resistance.

## 5.2

## Basic Measurement I (voltage and current polarity)

## Quantity

## Measured Value

ER1

14.49 V

VR1

5.42 V

VR2

9.56 V

IR1

11.70 x 10-3 A

IR2

11.70 x 10-3 A

Table 5.2a: Experimental results of voltage and current values across power supply, R1 and R2

## Quantity

## Calculated Value

ER1

15.00 V

VR1

5.47 V

VR2

9.53 V

IR1

11.6 x 10-3 A

IR2

11.6 x 10-3 A

Table 5.2b: Theoretical results of voltage and current values across power supply, R1 and R2

Table 5.2c: Calculation for theoretical results of voltage and current values across power supply,

R1 and R2

## 5.3

## Basic Measurement II (voltage reference point)

## Quantity

## Measured Voltage, (V)

## Calculated Voltage, V

## E1

14.99

15.00

## VR1

2.24

2.28

## VR2

3.90

3.98

## VR3

8.71

8.74

## VA

14.99

15.00

## VB

12.66

12.72

## VC

8.73

8.74

## VD

0.00

0.00

## VAB

2.33

2.28

## VBC

3.93

3.98

## VCD

8.73

8.74

## VDC

-8.73

-8.74

## VCB

-3.93

-3.98

## VBA

-2.33

-2.23

Table 5.3a: Theoretical & Experimental results of voltage across resistors and nodes on circuit

## Figure 5.3

## Resistor

## Voltage, V

## Theoretical

## Resistor R1

## Resistor R2

## Resistor R3

VA=VAD

=E1

=15V

VB=VBD

=VBC+VCD

=3.98+8.74

=12.72V

VC=VCD

=8.74V

VD=Ground

=0V

Table 5.3b: Theoretical & experimental results of voltage across resistors and nodes on circuit

## 5.4

## Basic Measurement III

## Quantity

## Calculated value

## E1

15.00V

## VR1

5.47V

## VR2

9.53V

## IR1

1.16 x 10-6 A

## IR2

1.16 x 10-6 A

Table 5.4a: Theoretical results of voltage and current values from power supply, R1 and R2

## Quantity

## Measured value

## E1

14.89V

## VR1

4.09 V

## VR2

7.44 V

## IR1

1.0 x 10-6 A

## IR2

1.0 x 10-6 A

Table 5.4b: Experimental results of voltage and current values from power supply, R1 and R2

Table 5.4c: Calculation for theoretical results of voltage and current values from power supply, R1 and R2

## 6.0 Discussion

## 6.1.1 From the Graph plotted, comment on the verification of Ohm's Law.

Based on the graph of voltage against current, the value of measured and calculated are shown as below,

The measured resistance,

= 457.67 ï-

The calculated resistance,

= 468.75 ï-

Note: Resistance, R is the gradient of the graph, m.

Based on Ohm's Law, the potential difference is directly proportional to the current provided that the temperature constant. Although the calculated resistance is slightly larger than the measured value, Ohms' Law is still verified.

Calculated Resistance (468.75 Ohm) > Measured Resistance (457.67 Ohm )

## 6.1.2 Tabulated results on a results page comparing the measured and theoretical values for Figure 1.4 (Lab Manual) to give a direct comparison. Comment on reasons for variations between theoretical and practical results for each section of the laboratory.

Based on Figure 1.4, there is a slight different between the two potential differences, V between the calculated and measured value based on Basic Measurement II in Data & Results part. The causes of differences of voltage are as follows:

I) Wire is heated up

II) Multimeter is not functioning well as it detects air as voltage when there is air friction.

III) The resistor quality. This is because each resistor has different quality and has different tolerance.

## 6.1.3 Tabulated results on a results page comparing the measured and theoretical values for Figure 1.3 and 1.5 (Lab Manual) to give a direct comparison. Comment on reasons for variations between theoretical and practical results for each section of the laboratory.

Based on Figure 1.3 and 1.5, the results are relatively close. There is only a slight change in value between the two potential differences, V based on Basic Measurement I & III in Data & Results part. The causes of voltage differences are as follows:

I) Wire is heated up

II) Multimeter is not functioning well as it detects air as voltage when there is air friction.

III) The resistor quality. This is because each resistor has different quality and has different tolerance.

## 6.1.4 What precautions need to be taken when measuring high ohmic value resistors with

## Digital Multimeter (Why?)

While measuring high ohmic value of resistor using Digital Multimeter, we need to be sure that there is no other voltage present in the circuit. Apart from that, at least one end of the resistor has to be disconnected from the circuit to prevent the rest of the circuit resistance in parallel with it.

## 6.1.5 What caused the errors when measuring voltages of the circuit of Figure 1.5?

One of the possible errors would be the wire since it would heat up easily when huge amount of voltage is used. Another error would be the multimeter because the multimeter detected a value changes when there was a friction between the air and the clip of the multimeter.

## 6.6.6 What would be the effect on the circuit Figure 1.5, if the ammeter was placed across

## resistor R1 to measure current in the circuit?

The ammeter has its own internal resistance. In a series circuit, when the ammeter is placed across the resistor, R, the resistance of the circuit will be more higher because RT = (R1 + R2 + r). Thus, the current of the circuit will be smaller as resistance is higher. This verifies the Ohm's Law (Current up, resistance down).

## 7.0

## Conclusion

From the laboratory which four different experiments were conducted, it could be concluded that in a basic DC circuit, some of the principles or laws such as the Ohm's Law, Kirchoff's Law and Divider Rules could be applied for circuit analysis and problems solving. The electrical instruments were to be connected or hooked in the correct manner to obtain accurate measurements or data. Although the measurements or readings had slightly distinct from the theoretical results due to the minor errors while conducting the experiment or the interference of neglect able internal resistance present within the circuit, the interrelationship between the variables such as the voltage, current and resistance in a circuit could be proven, thus verifying the laws and rules used in the circuit analysis tasks.

## Appendix

Ohms' Law:

Circuit Analysis:

= (For resistors in parallel)

(For resistors in series)

Voltage Divider Rule