-397572453170Faculty

-397572453170Faculty: Faculty of Science and Engineering
Department: Department of physics with material sciences
Academic Year: 2018/2019
Module: Electromagnetic Fields and waves
Assessment: CW1: DC circuit
15.11.2018
Faculty: Faculty of Science and Engineering
Department: Department of physics with material sciences
Academic Year: 2018/2019
Module: Electromagnetic Fields and waves
Assessment: CW1: DC circuit
15.11.2018
0-635
DC circuit lab measurements.
Abstract
This experiment confirmed the ohm’s law by determining the relationship between current and voltage in certain values of resistance. As well as comparing the calculated and measuring values of currents and voltages connected in parallel and series in DC circuit which were nearly close. Moreover, the verification of superposition theorem was approved in this experiment, there were significant differences between the calculated and measured values due to numbers of error. A capacitor of 100 µF was charged and discharged and taking the value of current and voltage every 5 sec. Furthermore, different graphs of voltage and current against time when the capacitor charging and discharging were plotted.
Introduction
An electrical circuit is a union of components are connected whether in series of parallel by wires in a certain path. There are two types of electrical circuit AC and DC. However, this lab will be concentrating on DC circuit which is has the current flow in one direction only (All about circuit, ND). FIGURE1 shown a simple DC circuit:

Figure1- simple DC circuit.

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The relationship between the current I (A) which is the flow of charge in a conductor per unit of time (t) with the ability of charge to do work which called potential difference voltage V (V) and the resistance R which is the opposition of current flow is ohm’s law

?=VI (1)
R: resistor, (ohms ?)
V: voltage (volt, v)
I: current (amperes, A)
The resistors in any circuit can be connected in series and parallel,
Resistors in series:
FIGURE2 shows 3 resistors are connected in series in a close circuit the current flows through each resistor, which means that the current is the same in R1,R2 and R3,
IT=I1=I2=I3 (2)
However, the total voltage will be the sum of each voltage across the circuit,
VT=V1 +V2+V3 (3)
From (2), (3) the total Resistance is the sum of individual resistance,
RT=R1+R2+R3 (4)
1893736-1765300
Figure2- series connection
Resistors in parallel:
FIGURE3 shows the parallel connection. The current will supplied into I1,I2 and I3 each flowing through R1,R2 and R3 and the sum of them is total current IT (Faizaan, ND) ,
IT=I1+I2+I3 (5)
And the voltage across each resistor will be equal,
VT=V1 =V2=V3(6)
So,
1RT=1R1+1R2+1R3 (7)

Figure3- Parallel connection.

Moreover, Superposition theorem is a way to simplify a complex circuit with 2 or more power source by replacing one source with short circuit and solve for voltage and current then, the same process will be applied with the other one. Finally, algebraic sum of the currents and voltages is the final values of current and voltage (Circuit globe, ND). However, a capacitor is the device that store charge (Beaty, 2014). The time taken to charge and discharge a capacitor called time constant.

?=R×C (8)R: Resistance (ohms, ?)
C: Capacitance (Farad, F)
Moreover, the capacitor discharge 37% of its original value as shown in FIGURE4.
170942016065500
Figure4- Curve of charging and discharging the capacitor
This lab experiment is intended to confirm the ohm’s law and superposition theorem, compere the calculated and measured values of voltage and currents in DC circuit connected in parallel and series, Finally, DC charging and discharging a capacitor will be examined.
Methodology
Materials
DC power supply
Breadboard
Digital multimeter
Resistors (0.44, 2.2,330.390,2×680, 820, 100k? and 3×1000 ?)
Capacitor 100 µF
Timer
Procedure
Part1: ohm’s law
The experiment was set up as shown in FIGURE5 with resistor of 470 ? then, using the colour code given in the lab script the colour code of the resistor was estimated and measured the correct value of the resistor using the multimeter after set it to voltimeter. Next the values of current when the Dc power was set it to 1V was measured and noted in TABLE1 the value of voltage was increased by 1Vuntil 8v and record the values of current. However, this process was repeated for resistor 2.2k? and 10k?. Finally TABLE1, 2 and 3 were plotted.
15525756350
Figure5- ohm’s law experiment set up
Part2:
The experiment was set up as shown in FIGURE6. Then the colour code of each resistor were estimated and measured as well as recorded in TABLE4. After that the values of each voltage and currents were calculated using ohm’s law. Then, the values of voltage and current were measured via voltmeter connected across the circuit and ammeter connected through the circuit and recorded them in TABLE5.

Figure6- Parallel-series DC circuit set up experiment

Part3: superposition theorem.

1359535143319500The experiment was set up as shown in FIGURE7, then the values of resistor were measured and recorded in TABLE6. The values of IA, IB AND IC were measured using ammeter connected through the circuit and noted in TABLE7. Moreover, the power source of 12v was removed and replaced with a wire then, the values of each I in the circuit were measured and calculated as well as noted. After that, the 10 v was replaced with short circuit and connected the 12 v again and measured the values of I flowing in the circuit and calculated using the same equation used previously. Finally, each values of current with same Brach were added and noted.

Figure7- superposition theorem experiment set up
Part4: charging and discharging a capacitor.

The circuit was set up as shown in FIGURE8 and the values of R and the capacitor were measured. The dc power supply was set to 10 V. Once the circuit was connected the capacitor start charging and the values of current and voltage were recorded every 5 sec until 60 sec and noted the values in TABLE14. After that the power supply was disconnected from the circuit which makes the capacitor discharged and record the values of current and voltages every 5 sec. Then, the VC and IC against the time were plotted for charging and discharging process. Next the time constant was calculated as well as values of VC and IC using VC=V (1-e-tCR) , VC=V e-tCR AND IC=I e-tCR .

1647825000Figure8- Charging and discharging a capacitor experiment set up.

Results
Part1: ohm’s law
V (V)
±0.005 1.05 1.98 3.03 4.02 5.03 6.03 7.04 7.99
I (mA)
±0.005 2.25 4.25 6.52 8.66 10.79 13.01 15.22 17.28
Table1- The current flow through circuit with 470 ?V(V)
±0.0005 1.144 2.134 3.212 4.246 5.192 6.248 7.282 8.316
I(mA)
±0.005 0.52 0.97 1.46 1.93 2.36 2.84 3.31 3.78
Table2- The current flow through circuit with 2.2k ?
V (V)
±0.0005 1.010 1.985 3.002 4.031 5.001 5.984 7.027 8.053
I (mA)
±0.005 0.09 0.19 0.3 0.4 0.5 0.6 0.7 0.81
Table3- The current flow through circuit with 10K ?

22860028321000
Note that the error bars are too small to be seen.
Part2: series- parallel dc circuit.

Resistor R1 R2 R3 R4 R5
Colour code Orange, orange, brown, gold. Brown, black, red, gold. Blue, Gray, brown, gold. Yellow, violet, brown, gold. Orange, white, brown, gold.
Exact value 330? 1000? 681? 470? 390?
Table4-Values of resistor
Calculated
Measured
±0.005
VR1 0.60V 0.50V
VR2 0.0023×10-3V 0.002×10-3V
VR3 1.36 V 1.54 V
VR4 0.94V 1.07 V
VR5 0.71V 0.82 V
IT 1.83mA 2.55 mA
I1 2.30 mA 2.22 mA
I2 2 mA 0.21mA
Table5- values of current and voltage.

Part3: superposition theorem.

R1(?) R2(?) R3(?)
680 820 1000
Table6- Value of resistors
IA(mA)
±0.005 IB(mA)
±0.005 IC(mA)
±0.005
13.08 0.701 5.75
Table7- measured values of current
I1(mA)
±0.005 I2(mA)
±0.005 I3(mA)
±0.005
13.15 11.63 1.43
I1(A) 12(A) I3(A)
0.0088 0.0040 0.0048
Table8- values of current / measured
Table9-Calculated values of current
I4(mA)
±0.00005 I5(mA)
±0.00005 I6(mA)
±0.00005
13.5700 14.8960 0.0016
Table10-measured value of currents
I4(A) I5(A) I6(A)
0.010A 0.004A 0.006A
Table11- calculated value of currents
IA=I1-I6 IB=I4-I3 IC=I2+I5
13.15(mA) 12.14(mA) 26.53(mA)
Table12-Sum of currents/measured
IA=I1-I6 IB=I4-I3 IC=I2+I5
0.0028(A) 0.0052(A) 0.0080(A)

Table13-sum of currents/calculated
Part4: charging and discharging of capacitor
Charging
Time VC (V)
±0.00005 IC(?A)
±0.005
0 0.0024 0
5 0.9475 11.72
10 1.4085 7.28
15 1.6843 4.49
20 1.8497 2.81
25 1.9766 1.58
30 2.0223 1.09
35 2.0541 0.77
40 2.0708 0.61
45 2.0849 0.47
50 2.0908 0.37
55 2.0959 0.33
60 2.0983 0.31
Table14-Current and voltage values of charging the capacitor
Discharge
Time VC
±0.0005 IC
±0.005
0 2.0520 0
5 1.6761 16.97
10 0.8905 9.01
15 0.5389 5.45
20 0.3288 3.24
25 0.1997 2.10
30 0.1182 1.23
35 0.0748 0.76
40 0.0461 0.50
45 0.0295 0.33
50 0.0194 0.21
55 0.0125 0.13
60 0.0085 0.09
Table15-current and voltage of discharging the capacitor

Calculations:
Part1
According to ohm’s law equation-
V ?I?R=VIUsing the equation of the line-
y=mx+cRearranging this gives-
V=RI+CSo, the gradient of figure (9) (10) (11)-
m=R?m=VITable 1
Using the equation from the figure (9)
y=463.21x-0.0009So,
R=463.21 ?Table 2
Using the equation of the line from figure (10) –
y=220.21x-0.0182So,
R=220.21 ?Table 3
Using the equation of the line from figure (11) –
y=10046x-0.0098So,
R=10046?Part2
Using equation (4) to find the total resistance of R3 and R4
Rx = R3 + R4 = 680 + 470 = 1150 ?
Use equation (7) to find total resistance of RX, R2
Rm=1Rx + 1R2=Rm= 11150+ 11×10^3=534.884? Using equation (4) to find the total resistance of the circuit.
RT =Rm+ R1 + R5 = 534.884 + 330 + 390 = 1254.884?
Use ohm’s law to find the total current.
IT=VRT=2.31254.884=1.83 mAVR1:
VR1 = R1.IT = 330 × (1.83×10-3 ) = 0.6039 V
I1:
I1=VR2=2.31×103=2.3 mAI2:
I2=VRx=2.31150=2mAVR2 = (1×10-3) (2.3×10-3) = 2.3×10-3 V
VR3 = (2×10-3) (680) = 1.36 V
VR4 = (2×10-3) (470) = 0.94 V
VR5 = (1.83×10-3) (390) = 0.7137 V
part3
step1:
Find the voltage produced by 10v by replacing 12v by short circuit,
RT = R1 +R2×R3R2+R3= 680 +(820)×(1×103)820+(1×103)= 1130.5?
I1=VRT=101130.5=0.0088 AI2 = I1 ×R2R2+R3= 0.0088 ×820820+(1×103)= 0.0040 A
I1 = I3 + I2
I3 = I1 – I2
I3 = 0.0088 – 0.0040 = 0.0048 A
Step 2:
Now, replace 10 with short circuit and solve for 12v,
RT = R1×R3R1+R3+R2= (680)×(1×103)680+(1×103)+820= 1224.8?
I4=VRT=121224.8=0.010 AI5 = I4 ×R1R1+R3= 0.010 ×680680+(1×103)= 0.004A
I4 = I6 + I5
I6 = I4 – I5
I6 =0.010 – 0.004 = 0.006 A
Part4-
Using equation (8)
?=100K×100??=10 secRereigning equation (8)
C=?RUsing the equation of the line
y=mX+c?=tln?(v)??=m=-1slopeFrom figure16 the line equation of the graph
y=-0.0949x+0.7971?m=-0.0949 s-1=-1slope=-1-0.0949=10.5 sC=?R=10.5100×103C=105KFDiscussion:
Ohm’s Law
The connection of ohm’s law experiment was set up as shown in FIGURE5 to estimate the relationship between I and V with different values of resistances (470?, 2.2k?, 10k?). It is clear from FIGURE 9, 10 AND 11 as the voltage increases the current increases which demonstrates a directly proportional relationship between voltage and current. Which represent the ohm’s law as defined above. Furthermore, the experimental values are slightly different from the calculated values for resistance 10k.That is due to uncertainty error happened during the experiment. However, the values that gained from the experiment when the resistance was 470 and 2.2k were nearly the same from the calculated values as it is clear from figure 9 AND 10 the measured line is close to the calculated values for resistance 470 and 2.2k. Moreover, as the value of resistance increases the current decreases, the current flowed through the circuit of 470? when the voltage 1 was 2.25A however 0.09 A flowed when the circuit was conceded with 10k?. This because the resistor is opposes the flow of current so, as the value of resistance increases the current decreases. As shown from the equations of graph (9) (10) (11) the gradient represent the value of resistor. The measured value (463.21?) of the first gradient was slightly different from the theoretical value which is (470?).This experiment was successfully approved ohm’s law.
Series – parallel DC circuit
The calculated values were slightly different from the measured values. The measured values of VR3,VR5 were not close enough from the calculated values this due to absolute errors in measurement as changing the voltammeter across value of resistor to the other one caused shot which had a strong effect on the values. However, the values of current were not close to the calculated values. There are several explanation for this, but the most likely one is that the connection of the Ammeter was wrong because we had to breakdown the whole circuit to connect the Ammeter to measure each value of current which cause lots of confusing. In this experiment 2.3 v was used by mistake instead of 20 v. indeed in all the calculation 2.3v was used not 20 v. Using ( P=VI ) the values of power in each resistor are shown followed table. However, the energy used if the circuit was connected 2 weeks is 44271.36 J
E=Ptot. t E=(0.0366)(2×7×24×60×60)E=44271.36 JPT 0.0366 W
PR1 0.00138 W
PR2 4.6 ×10-10 W
PR3 0.00272 W
PR4 0.00188 W
PR5 0.00131 W
Although this experiment had some sources of error due to the reasons stated above, it went successfully.
Superposition theorem
FIGURE8 shows the circuit of this experiment which have 2 source of EMF12V and 10V. This type of circuit cannot be solve directly using ohm’s law. Superposition theorem is a way to investigate any circuit by connect one source of voltage with a short circuit and solve for the other one then do the same thing with the other source of voltage and the sum of both values are the final values of current of the circuit. The calculated values of currents were not close enough to the measured values due to experimental errors, the connection of the circuit was not easy to connect and many mistake in connecting the circuit had been made which has effect on the values as well as I changed the value of voltage by mistake which had a strong effect on the accuracy of the values. The experiment should be repeated to get more accurate values. The superposition theorem can be applied with any circuit that have 2 or more sources as stated in (circuit globe, ND).

Charging and discharging the capacitor
After conducting the experiment, the experimental values of capacitance C (105?f) which is slightly different from the theoretical value (100?F). The (-1slope) is represent the time constant which is the time taking to charge/ discharge the capacitor. It is clear from FIGURE12 the capacitor has been charged to 63% of its final value and the voltage dropped to 37% of its original value. When the capacitor started to charge the voltages increases and the current starts to flow through the circuit until the voltage reached to zero so, the capacitor is fully charge as it is clear from FIGURE12. However, when the circuit was disconnected from the power supply the voltage across the circuit started to increase which makes the current flow and the charges starts to flow again from the capacitor until the capacitor is fully discharge (All about circuit, ND), FIGURE12,13,14 are shown this processes. The differ in the calculated and measured values might due to absolute error in measurement as well as heating up the weirs the resistance of the resistor could increase and the cell of capacitor could decrease their capacity due to chemical processes. Finally, not letting the capacitor to fully charge is one of the main fault.
Improvement
It would be not possible to limit the errors in this experiment, repeating the experiment is one of the way to decrease the errors and get more accurate results. Avoiding the shot by using bigger breadboard to connect the weirs not close to each other so by doing this loops are avoided. Moreover, using read weirs for + sign and black weirs for – sign is reasonable to avoid getting confuse. To avoid heating the resistor in part4 decreasing the power supply is a possible solution. Finally, the experiment must done in a prober place where no chemical process can affect the result.
Conclusions
The data of the first part of the experiment suggested that there is directly a relationship between voltages and current as shown in FIGURE9, 10 AND 11 which is approve ohm’s law. The slope of the graphs are represent the values of resistance which were close to the calculated values (463.21? for 470?), (220.21? for 2.2k) and (10046? for 10k?). Moreover, the calculated values of series-parallel DC circuit were slightly different from the measured values this due to error in measurement as stated above. However, the third experiment successfully approved the superposition theorem. Indeed, some of the calculated values were close to the measured values. The time constant of charging and discharging 100?F capacitor was 10 s as it is clear from the invers slope of figure16. The aims of this experiment were met successfully.
References
All about circuit. (ND). Ohms law. Retrieved from
https://forum.allaboutcircuits.com/threads/ohms-law.121300/All about circuit. (ND). Capacitor Charging and Discharging. Retrieved from
https://www.allaboutcircuits.com/textbook/experiments/chpt-3/capacitor-charging-and-discharging/Beaty, D. (2014). The Gale Encyclopedia of Science: Capacitance. p766-768. Retrieved from http://go.galegroup.com/ps/i.do?p=AONE;u=chesterc;id=GALE%7CCX3727800435;v=2.1;it=r;sid=summonCircuit globe. (ND). Superposition Theorem. Retrieved from

Superposition Theorem


Faizaan, A. (ND). Electrical Academia: Series Parallel Circuit | Series Parallel Circuit Examples. Retrieved from
http://electricalacademia.com/basic-electrical/series-parallel-circuit-series-parallel-circuit-solved-problems/

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