Alexandria University
Faculty of Engineering
Electrical Engineering Department
3rd year communications
HSx12 - Technical Writing
21/12/2020
Technical Report
Voltage and Current in Series and Parallel DC Circuits
Name: Mahmoud Fawzy Taha-Elaraby
Sec: 6
ID: 202
1
Table of contents
Cover
1
Table of contents
2
introduction
3
Parallel connection
4
Series connection
6
conclusions
8
Appendix
9
References
10
2
Introduction
-Electricity became one of the tools in our lives that we cannot live
without it anymore. So, studying electricity has become essential in this
era. And the beginning of studying electricity is to study Elec-Circuits.
The first topics in any circuits course contain few main things such as:
•
•
•
•
The 2 main types of Electricity & Sources (DC & AC).
The basic discrete elements (R, L, C).
Ohm’s law (the main law in electricity).
Connecting elements using parallel & series connections.
- this report we will discuss the parallel & series connections in DC
(direct current) circuits using only resistors (R). Which they are the
easiest case among the other cases (using AC or a combination of other
elements together).
-In brief, the electricity is mainly a form of power/energy which is
represented in 3 main components: 1- Current(I): the flow of charges moving in the cable (A)
2- Voltage(V): the work needed to move the charges in the cable (V)
3- Resistance(R): the opposition that resists the flow of charges (Ω)
-Ohm’s law connects these 3 physical quantities in a simple form(V=I*R)
-DC is a constant-valued& one-directional electricity with time.
-Resistors are 2-terminal components that have a constant value of
resistance at room temperature &for any value of I & V.
3
1- Parallel connection
• Parallel connection (shown in figure) is that
each resistor is connected with its 2 terminals
with the other resistor by its 2 terminals.
• The rule to calculate the total resistance is
1
1
1
1
= 𝑅1 + 𝑅2 + 𝑅3
𝑅t
Rt= 6/11 kΩ
1.1 Voltage Calculations
• Theoretically, all resistors are connected to the same 2 terminals.
and the voltage drop is between these 2 points, voltage on each
resistor should be the same. (V(between 2 connection points)=V1=V2=V3)
• practically (as we see in the 2 figures below),
V1(source voltage) =VR1=VR2=VR3=12V
• the results are the same whether resistors are equal or different.
4
1.2 Current Calculations
• Theoretically, all resistors are connected to the same 2 terminals.
and since the more current at a junction moves the easier way,
the current will flow in all the resistors and the current value in
each resistor is dependent on a Current divider ratio between the
resistor’s resistance and the total resistance. IR1 = It*(Rt/Rt+R1)
• practically (as we see in the 2 figures below),
It = V/ Rt = 12 / (6/11) =22mA
IR1 = It*(Rt/Rt+R1) = 12mA
IR2 = It*(Rt/Rt+R2) = 6mA
IR3 = It*(Rt/Rt+R3) = 4mA
In case of equal resistors,
The current will be the same.
Rt =2/3 Ω
It = 18mA
IR = It*(Rt/Rt+R) = 6mA
= It / NR = 6mA
5
2- Series connection
• Series connection (shown in figure) is that
each resistor is connected along a single
conductive path. Terminal by terminal
• The rule to calculate the total resistance is
Rt=R1+R2+R3 Rt= 6 kΩ
2.2 Voltage Calculations
• Theoretically, all resistors are connected along the same path. and
the voltage drop is between the start & end of this path, voltage
will be divided on all the series resistors with a ratio between the
resistor’s resistance and the total resistance. VR1 = Vt*(R1/Rt)
• practically (as we see in the 2 figures below)
VR1 = Vt*(R1/Rt) = 2V
VR2 = Vt*(R2/Rt) = 4V
VR3 = Vt*(R2/Rt) = 6V
In case of equal resistors,
The voltage will be the same.
VR1 = Vt*(R1/Rt) = 4V
6
2.2 Current Calculations
•Theoretically, all resistors are connected to the same 2
terminals. and the voltage drop is between these 2 points, voltage
on each resistor should be the same.
It (total current) = IR1 = IR2 = IR3 = V/ Rt = 12 / 6 = 2mA
•practically (as we see in the 2 figures below),
•the results are the same whether resistors are equal or different.
7
Conclusions
• in parallel circuits, voltage is the same.
• in parallel circuits, current divides by current divider rule.
• in series circuits, voltage divides by voltage divider rule.
• in series circuits, current is the same.
8
Appendix
EIA Standard Resistor Values by ± Tolerance%
Move the decimal point to achieve the actual value desired.
E6
E12
E24
± 20% ± 10% ± 5%
E48
± 2%
100
100
105
100
110
110
115
100
121
120
127
120
133
130
140
147
150
154
150
162
160
169
150
178
180
187
180
196
200
205
E96
± 1%
100
102
105
107
110
113
115
118
121
124
127
130
133
137
140
143
147
150
154
158
162
165
169
174
178
182
187
191
196
200
205
E6
E12
E24
± 20% ± 10% ± 5%
E48
± 2%
215
220
226
220
237
240
249
220
261
270
274
270
287
300
301
316
330
332
330
348
360
365
330
383
390
402
390
422
430
442
210
9
E96
± 1%
215
221
226
232
237
243
249
255
261
267
274
280
287
294
301
309
316
324
332
340
348
357
365
374
383
392
402
412
422
432
442
453
E6
E12
E24
± 20% ± 10% ± 5%
E48
± 2%
464
470
487
470
511
510
536
470
562
560
590
560
619
620
649
681
680
715
680
750
750
787
680
825
820
866
820
909
910
953
E96
± 1%
464
475
487
499
511
523
536
549
562
576
590
604
619
634
649
665
681
698
715
732
750
768
787
806
825
845
866
887
909
931
953
976
References
1- Wikipedia.com
2- NI Multisim Software.
3- Charles Alexander, Matthew Sadiku - Fundamentals of Electric
Circuits.
4- https://www3.nd.edu/~jott/measurements/Sensors/Standard_Re
sistor_Values.pdf
10