Electrical Measurements in the Laboratory Practice - Lab Report Example

Abstract

The purpose of this experiment was to understand the difference between series and parallel circuits in terms of the voltage, current, and resistance, ; to compare the circuit experimental results with those obtained by using theoretical approach and ensuring that hands-on experience while working with resistor circuits is attained. The aims were achieved through the arrangement of three resistances in series and in parallel: 1000Ω, 820Ω, and 680 Ω and measuring their respective current and voltage flowing through them using DMM set. Additionally, the parallel and series circuits were connected to 10V and 15V dc supply for parallel and series circuit respectively. From the experiment, the series circuit results indicated that current flowing through each resistor was equivalent to the current flowing through the entire circuit which measured 6mA while the total circuit resistance was 2500 Ω. The effective resistance for the series circuit was found to be the total sum of the individual resistances that is 1000Ω + 820Ω +and 680 Ω = 2500 Ω. However, the voltage across each resistor varied at: 1000 Ω= 5.972V; 820 Ω = 4.972V; and 680Ω =4.131V. Conversely, the parallel circuit was characterized by identical voltages across each resistor at 10V. Additionally, the effective resistance of the parallel circuit was measured to be 270.995Ω. However, the current across each resistor was different as: 1000 Ω = 10.00mA; 820Ω= 12.195mA; and 680Ω=14.706mA and the total current for the circuit was 36.90A.

Introduction

Greene & Heniford defined voltage as the electric potential energy per unit charge with a standard unit of volts (V). Current, according to Greene & Heniford , is the rate of flow of charge across a conductor with SI units of Amperes (A). Greene & Heniford define resistance as the ratio of voltage to the electric current flowing through a conductor and SI units of Ohms (Ω).

According to Rawlins & Fulton series circuits are those where devices or components’ connection is end-to-end to form a single path through which the current in the circuit flows. The current flowing across each device is identical and the effective resistance in the circuit is the sum of individual resistance through each device. Rtotal = R1 + R2 + ….+ Rn. Rawlins & Fulton defined parallel circuits as having all devices and components arranged in a way that connection of one component is across the connection of another, thereby forming two sets of electronically shared points such as heads are connected together and so are the tails. In parallel circuits, the voltage across each device is identical and also equal to that of the entire circuit. However, current differs as it breaks up and some flow along each parallel path only to recombine where the branches join again in accordance to Kirchhoff’s first law.

Sang and Jones definition of Kirchhoff’s first law is that the sum of current flowing through a junction is zero. Kirchhoff’s second law is where the total voltage across a closed circuit network is equivalent to the sum of the voltage drops within the closed circuit and which is equivalent to zero. Simply put, the sum of voltages within the closed circuit is zero.

Rawlins & Fulton defined Ohms law as stating that the current flowing through a conductor is proportional to the potential difference between its end, provided that temperature and other physical factors remain at constant, VαI where the constant of proportionality is the resistance, R = V/I. The SI units are ohms (Ω).

Method

Method I

Figure 1: A three resistor Series Circuit for the experiment

Figure 2: A three resistor parallel circuit for the experiment

Method II

Series circuit

For the series arrangement, the circuit was connected as shown in figure 1 above. With the use of the DMM, the output voltage was adjusted to 15V. The DMM was also used to measure the total resistance of the circuit, the resistance and the current flowing through each resistor in the circuit. The value were recorded in table 1 and 2 as shown below.

Parallel Circuit

The parallel circuit was connected as in figure 2 above, to a 10V dc supply, and using the DMM, the total resistance of the circuit was measured and recorded. Additionally, the DMM was used to measure the currents labled 1a, 1b, 1c , and 1d associated to the circuit were also measured and recorded as shown in the tables 3 below.

Results

Series circuits

The table 1 below accounts for the percentage difference between the nominal resistance and the measured resistance in the series circuit results.

Nominal Resistance (Ω)

Measured Resistance (Ω)

% Difference

R1= 680

679.7 aver

0.04

R2=820

809.1 aver

1.33

R3=1000

982.95

1.171

Series Rtotal = 2500

2475.65

0.97

Table 1: Test results for the nominal resistance against measured resistance in the series circuit

Quantitiy

Measured value from DMM

Theoretical values

% Difference

VS

15.034

15

0.23

Rtotal

2475.65

2500

0.97

VR1

4.1307

4.08

0.05

VR2

4.972

4.92

0.14

VR3

5.972

6

0.46

IA

6.066

6

1.13

IB

6.08

6

1.1

IC

6.065

6

1.08

ID

6.068

6

1.13

Table 2: Table of measured values of V, I and R including their % differences

Parallel Circuit

The table 2 below also accounts for the percentage difference between the nominal resistance and the measured resistance.

Quantity

Measured value from DMM

Theoretical calculated values

% difference

Vs

10.03

10

0.30%

VR4

10.023

10

0.23%

VR5

10.023

10

0.23%

VR6

10.023

10

0.23%

Ia

37.2

36.90

0.81%

Ib

10.206

10

2.06%

Ic

12.369

12.195

1.43%

Id

14.777

14.706

0.48%

Rtotal

269.03

270.995

0.73%

Table 3: Test results for parallel circuit

Discussion

Series Circuit

From the series circuit results, the voltage across each resistor is different at VR1=4.1307V, VR2 = 4.972V, and VR3 = 5.972V, while the current across each resistor was IR1 = 6.066A, IR2 = 6.08A, IR3= 6.065A, and Itotal = 6.066A. The values of V, I, and R measured by the DMM and the nomial values for V, I , and R for the series circuit had insignificant variations within 5% margin of error. Consequently, they agreed with theory.

From the experiment results, there was a difference between the nominal resistance and the measured resistance. However, the differences were within the acceptable +/-5% tolerance. The differences in the measured resistance were due to the fact that resistors are sold with a certain tolerance and it is not guaranteed that they are closer to the specific stated value. Normally, resistance tolerance falls within 1%, 5%, 10%, and 20%, and the more accurate resistors are sold at higher prices.

From the experiment, the sum total of voltages across all devices is 15v which is equivalent to that of the entire circuit. As a result, the sum voltages in the closed circuit is zero in accordance to Kirchhoff’s second law. Additionally, it is evident that the measured potential difference across each resistor differed from that of the nominal voltage across each resistor. The differences are attributed to the resistance due to the heating of the wires which is affected by physical factors like temperature and pressure.

Parallel Circuits

From the results, it was noted that the potential difference across each resistor was identical and was equivalent to the circuit total voltage of 10V. However, the current across each resistor was different, while the sum total of the three currents was equivalent to the total current in the circuit in accordance to Kirchhoff’s law. The results are consistent to the theory that current in parallel is difference across each device while potential difference across each device in the circuit is identical and equal to the circuit total voltage.

The DMM result of the measured resistance was 269.03V while that of the theoretical was found to be 270.955V. The difference in voltage between the two values was 0.74%. Since voltage is given by V=Itotal Rtotal, the resistance of the wire due to heating is associated to the variations in Itotal, while resistor tolerance accounts for variations in Rtotal.

The improvements include ensuring that the physical factors such as temperature and pressure in the laboratory are held at a constant. This can be achieved through the use of very low currents to minimize heating. The voltage to be used must be smoothened. Additionally, the circuit must have a switch such that the current is only switched on when needed. Finally, using higher resistance is recommended to allow for greater variations in the readings.

Conclusion

The experiment results indicate that when voltages across circuit components are identical, the components are connected in parallel. In such arrangement, currents are different in each component but always sum up to the total current in the circuit according to Kirchhoff’s first law. Conversely, when the currents through each circuit component are identical, the components are connected in series. In such arrangement, the potential difference across each component is different but the summation of the voltage across the closed circuit is zero in accordance to Kirchhoff’s second law.

Appendix

Series circuit calculations

From ohms law:

Parallel circuit calculations

Voltage across all the resistors is equivalent to the circuit total which is 10v

Total current in the circuit is given by ohms law: