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# Lab report 2

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### Lab report 2

1. 1. Introduction Electricity is an essential part of the modern life experience, and as an engineer it is essential to know how it behaves and responds to changes in its trajectory. This lab was divided into two major parts namely part 1 were you will verify Ohm’s law by developing a variation of voltage (V) against current (I) characteristic of a Resistor. Part 2 determine the current and voltage through current dividers and voltage dividers. The main goal of this lab is to be able to verify ohm`s law and to analyse simple resistive circuits, to measure circuit properties like (Voltage, Current, Power) of various elements in a circuit connected in series and parallel. In addition the knowledge to construct current dividers and voltage dividers will be gained and ways to determine unknown resistances will be gained as well. Theory Basic definitions needed for the complete understanding of the content of this report:  Voltage is electrical potential energy per unit charge which is measured in joules per coulomb which has its SI unit as volts.  Resistance is defined as the opposition within a conductor to the passage of electric current which has its SI unit as Ohms (Ω). Carbon resistor are the components which are placed in a circuit to oppose current flow.  Power supply is a device that supplies electric power to an electrical load.  Three different ways to express the relationship between, voltage, current and resistance. V=IR (1st way) I=V/R (2nd way) R=V/I (3rd way) Tolerance Colour Codes No Band = 20%; Silver = 10 %; Gold = 5% and Red=2%.
2. 2. Pre-lab Pre-lab questions Question 1  What is the power dissipated in a resistor?  Does it depend on the polarity of the source? Answers  Power dissipated  The power dissipated in a resistor has a relationship with the resistance and the current through that resistor. According to ohms law R=V/I but Power=V.I Voltage=R.I Therefore by substituting Power=R.I.I =RI2  Does it depend on the polarity of the source? These power does not depend on the polarity a negative sign will mean that power has been lost. Question 2  What is a voltage divider what is a current divider A voltage divider also referred to as a potential divider is a linear circuit that produces an output voltage which is a fraction of the input voltage. But voltage division refers to the partitioning of a voltage amongst the components of the divider when they are in series. Vt v1 R1 R2 V1=( R1/( R1×R2) ) × Vt
3. 3. Question 3  What is a current divider? Answer A current divider is a simple linear circuit that produces a current which is a fraction of its input current. Current division refers to the splitting of current between the branches of the divider. These components will be connected in parallel. The current divider rule... R1 I1 R2 I2 I Vt Rt= (R1*R2)/ (R1+R2) But V=IR and Total current I=V/ (Rt) I1= [R2/ (R1+R2)]*It and I2= [R1/ (R1+R2)]*It Question 4 By using figure 4 as an example circuit. Voltage across 4. Apply the knowledge you have about series and parallel connection of resistors to determine the effective resistance of circuits given in Figures 4 and 6 (use these resistance values R1 = 2.7-kΩ, R2 = 3.9-kΩ and R3 = 4.7-kΩ
4. 4. Assistant) between terminals P and Q as in the figure 3. Resistance in series RT=R1+R2+R3 2.7KN+3.9KN+4.7KN =11.3KN is the equivalent resistance Rt=[(R1 R2) R3 ] = (2.7KN*3.9KN)/(2.7KN+3.9KN) 4.7KN = (1.595KN*4.7KN)/(1.595+4.7KN) =1.19KN is the equivalent resistance Equipment used  Power supply  2 Digital Multimeter (DMM) which serves as a Voltmeter and Ammeter  Four carbon resistors with different resistances  Two conductors  Two banana conductors  Wire wound resistors (decade boxes).  Digital connection board
5. 5. Procedures To Measure Voltage: Change the voltage selection knob on the DMM to (DC or –V) for DC measureme nt. Voltage is measured in parallel with the load and the range of your measurement can be altered by using the Range buttons. To Measure Current: Change the current outlet of the DMM to (“+” terminal) and the COM outlet (ground). Current is measured in series you will have to break the circuit to measure current. For a current less than 200mA use the outlet (VΩA) and for current greater than 200mA use the outlet written 20A in red else the DMM will not be accurate and may not show the current reading. You can vary the range of your measurement by using the Range buttons. To Measure Power Supply Voltage: A voltmeter is always connected in parallel across your load or power supply. The “+” terminal of the voltmeter should be connected to the “+” terminal of the Power Supply hence forth referred to as (PS) (usually the red outlet) and the “-” terminal of the voltmeter to the “-” terminal of the PS (usually the COM or black outlet) of the DMM. Part 1 of the lab  Setup the circuit as illustrated in Figure 1.
6. 6. 1. Connect one of the connectors to the (DMM which is acting as an ammeter hence forth referred to as ammeter) as shown in figure 1. 2. The ammeter is connected in series with a resistor 3. Connect the (DMM acting as a voltmeter hence forth referred to as voltmeter) in parallel to the resistor and the ammeter. 4. Increase the output of the power supply from 0 to 10 volts, in steps of 1 volt increments. 5. Take voltage and current readings from the multi-meter and record your data in Table 1A. 6. Reverse the polarity of the power supply by interchanging the black and red terminals of power supply, 7. Repeat Step 4 until your voltage is at 10 volts. 8. Record the data in Table 1B. Part 2 of the lab  Obtain three resistors  Connect them in series as shown in the figure: 2 below.  Determine the resistance of the resistors by colour coding.  Measure the resistance with the voltmeter.  Record both the acquired values into (table 1).  Connect a 5-v Dc voltage supply between the terminals P and Q as in figure 2 above.  Take readings of VB-C , VA-B , VC-D , VA-D record these values.  Add all the values of V to calculate Vtotal.  Calculate the voltage across each resistor using equation labelled (1st way).  Compare both results.  Adjust the voltage in 5 steps as in table 2.  Measure the voltage across v1 v2 and v3. 
7. 7.  Connect the resistors in parallel as shown in figure: 5 above.  Replacing the R2 resistor with another resistor during.  Connect a 5-v Dc voltage supply between the terminals P and Q as in figure 2 above.  I1 (resistor 1), I2 (resistor2), I3 (resistor 3).  Make the following measurements I1, I2, I3.  Include an ammeter and calculate I across PQ.  Use ohms law to calculate the currents across R1, R2, R3 .  Record these acquired information on (table 2) Results Part 1 of the lab R1 colour coding, brown, black, yellow, gold R2 colour coding, yellow, violet, brown, black, gold R3 colour coding, red, violet, orange, gold R4 colour coding, orange, orange, orange, gold In series you use resistors 1, 2, 3 In parallel you use resistors 1, 4, 3 Resistor Value of resistance calculated from colour coding ranges Measured value or R resistance 1 100KΩ 98.9 KΩ R2 0,471KΩ 0.470KΩ R3 27KΩ 26.9KΩ RPQ 127.471KΩ 126.27KΩ Table: 1A
8. 8. Part 2 of the lab Resistors are connected in series 2.1: 126.27KΩ 2.1.2: VA-B= 3.9 V VB-C=0.018V VC-D=1.063V Measured voltage VA-D= VTOTAL=5.01 Measure resistance PQ= 126.27Ω Calculated total for voltage VA-B+ VB-C+ VC-D= 4.981v Voltage calculated using ohms law I= 39.1*10-6A V1=IR1= (39.1*10-6A)*98900Ω=3.86699v V2=IR2= (39.1*10-6A)*470Ω=0.018377v V3=IR3= (39.1*10-6A)*26900Ω=1.05179v V calculated total= v1+V2+V3 = 4.9363v VS, volts Across resistor R1, Across resistor R2, Across resistor R3, V1 V1/VS R1/RP Q V2 V2/VS R2/RP Q V3 V3/VS R3/RPQ 2 1.57 0.785 0.783 0.007 0.0035 0.2581 0.43 0.215 0.2130 4 3.16 0.79 0.783 0.014 0.0035 0.2581 0.84 0.21 0.2130 6 4.67 0.778 0.783 0.022 0.00367 0.2581 1.28 0.213 0.2130 8 6.22 0.7775 0.783 0.029 0.00365 0.2581 1.69 0.21125 0.2130 10 7.82 0.782 0.783 0.037 0.0037 0.2581 2.12 0.212 0.2130 Table: 2.1
9. 9. Resistors are connected in parallel Measurements Resistance between points P-Q = 12.8kΩ (Through resistor R1) I1= 49.9μA (Through resistor R2) I2= 148.3μA (Through resistor R3) I3= 178.6μA Ipq= 0.385 MA Current supplied by the source ITOTAL=49.9μA+148.3μA+178.6μA =376.8μA =0.3768MA I1=VPQ/R1=5/98900=50.556μA I2=VPQ/R2=5/32600=136.61μA I3=VPQ/R3=5/26900=185.87μA Itotal= 373.036 VS, volts IS, Amps mA Through resistor R1, Through resistor R2, Through resistor R3, I1 I1/IS R1/RP Q I2 mA I2/IS R2/RP Q I3 mA I3/IS R3/RPQ 2 0.15 0.02 0.133 7.726 0.060 0.4 2.5468 0.075 0.5 0.2130 4 0.31 0.04 0.129 7.726 0.122 0.3935 2.5468 0.149 0.4806 0.2130 6 0.46 0.06 0.1304 7.726 0.183 0.3978 2.5468 0.222 0.483 0.2130 8 0.62 0.08 0.1290 7.726 0.244 0.3935 2.5468 0.295 0.475 0.2130 10 0.78 0.100 0.1282 7.726 0.304 0.3897 2.5468 0.367 0.4705 0.2130 Table: 2.2
10. 10. Discussions Part: 1 of the lab Table 1 Table 2-- inverted polarity Dc readings Voltmeter Ammeter Dc readings Voltmeter Ammeter 0 0 0 0 0 0 1 1.01 0.55 1 -1.01 -0.55 2 2.02 1.1 2 -2.06 -1.12 3 3.04 1.65 3 -3.02 -1.64 4 4.06 2.21 4 -4.02 -2.19 5 5.01 2.73 5 -5.03 -2.73 6 6.01 3.26 6 -6.06 -3.3 7 7.05 3.83 7 -7.05 -3.83 8 8.01 4.35 8 -8.02 -4.36 9 9.05 4.92 9 -9.05 -4.93 10 10.01 5.44 10 -10 -5.44 Table: 1 Graph: 1 from table 1 Power supply voltage against measured voltage graph 0 1 2 3 4 5 6 7 8 9 10 12 10 8 6 4 2 0 0 2 4 6 8 10 12 Power supply voltage Measured voltage
11. 11. Graph: 2 from table 1 Graph3: from table2 Graph 4 table 2 6 4 2 0 Power supply voltage against current 0 2 4 6 8 10 12 Power supply voltage Current measured ( 0 -2 -4 -6 -8 -10 -12 Power supply against Voltage mesured with inverted polarity graph 0 2 4 6 8 10 12 Power supply voltage Voltage measured 12 10 8 6 4 2 0 Power from source (V) Power vs Current graph with inverted polaryties graph -6 -5 -4 -3 -2 -1 0 Current (I)
12. 12. According to graph 2 the slope of the line is determined by change in Y over change in x. Therefore 3.83-3.26 over 7-1= 0.57 Therefore the slope of the table with units will be 570 μΩ Ohms law did not exact predict the correct value of the resistor, since our voltage was directly proportional to our current as depicted by our linear graph shown above labelled graph2 from table: 1. For some reason if these resistor wouldn’t follow ohms law the line graph wouldn’t be straight but concave with a differing gradient along the line. The difference between the laboratory obtained values and the theoretical values is that theoretically, ohms law will give an exact value for the resistance and in a laboratory there is a small difference in the values due to properties like heat and internal resistance. Human errors could also occur during the recording of the data acquired during the experiment. Part 2 of the lab Series circuit 2.1 since we used the colour coding technic which is gives fairly acceptable results the resistances are fairly similar in the fact that according to table 1A above firstly all the results fall under the acceptable resistor ranges due to colour coding error. Therefore the difference is 127.471-126.27= 1.201 KΩ this is in the 5% range of error margin which all the resistors used contained and therefore makes sense in the experiment. 2.1.2 These voltage values that were calculated and the ones that were measured are very similar. These once again proves that the knowledge of ohms law is a very useful tool in the electrical field of studies. The measured value for Vtotal is 4.981V and the value for the Vcalculated with ohms law 4.9363V therefore the difference is 0.0447V. Once again these difference may be due to human error or other properties such as internal resistance.
13. 13. Parallel circuit 2.2.1 Due to the colour coding we used resistors 1, 4, 3 with the colour code of R1 colour coding, brown, black, yellow, gold R3 colour coding, red, violet, orange, gold R4 colour coding, orange, orange, orange, gold This will give a total resistance of 1/100+1/27+1/33=12.929KΩ Therefore the difference between the measured resistance 12.8kΩ and the calculated 12.929KΩ is 0.129KΩ. Once again these difference may be due to human error or other properties such as internal resistance. As you might have noticed this resistance is way smaller than the total resistance in a series circuit. 2.2.2 The measured currents have a total of 376.8μA and the calculated values have a total of 373.036. the values have a difference of 3.764 μA. This is a very small value it is equivalent to 0.000003764A which is very small. Once again these difference may be due to human error or other properties such as internal resistance. Conclusion In conclusion I have learned how to operate the DMM as a voltmeter and as an ammeter and further perfected my ability to make the use of colour codes to calculate the resistance of a resistor which is faster than actually measuring that resistance. The errors due to these calculations is very small and is within the range of resistivity of the resistor. There is also the matter of the conversion of electricity from one form to another that I have noticed while doing the last exercise in which the voltage readings are quite different from the real ones. This is due to the elements that contribute to the resistance namely (2.1(length of conductor, material of conductor, cross sectional area of the conductor and the material from which the conductor is made from). Ohms law is a very useful mathematical tool which can be used in the finding of theoretical values which are more or less the correct value with differences due to the above mentioned 2.1 properties. I also realised that. Furthermore I think that these findings were useful in the sense that I now understand more about electrical circuits than before and it helped me to understand the importance of parallel circuits as they drastically reduce the total resistance of a circuit. Lastly these lab and that it will contribute to the foundation of my overall engineering career by giving me a broad knowledge of all branches of engineering.
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