1. Electric Circuits

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CTSEET is the documentation website for courses offered by Dr. M. E. AlSharidah. It records all course descriptions, learning outcomes, objectives, syllabus, and notes.

70-115: Electric Circuits


2. Syllabus, outline , and guidelines

Description:

This course starts with presentation of source conversion. The chapters thereafter focus on the fundamental theorems of DC electrical network such as mesh analysis, nodal analysis, superposition, Thevenin's and Norton's theorems, maximum power transfer and finally Millman's theorem. The same theorems are repeated for AC electrical networks. Finally, methods for analyzing and calculating electrical quantities of balanced three-phase systems will be discussed.


Textbook:

Robert L. Boylestad, "Introductory Circuit Analysis".

2.1. Grades & Regulations - توزيع الدرجات و الاشتراطات

70-115: Elecrtric Circuits 1

% Category Notes
10 Atendance/Activity 2.5% will be deducted for every 4hr absense
30 Quizes Single problem quiz every 2 weeks
30 Midterm (Paper based) problem type questions 
30 Final Exam (Paper based) problem type questions

Important dates:

Event Date
Course starts Sun 2023-02-05
Last day of classes Thu 2023-05-11
Course ends Tue 2023-05-30
Assessment Date Topic
Quiz 1 Mon 2023-02-22 (DC) Superposition
Quiz 2 Mon 2023-03-08 (DC) [Thevenin or Norton]
Quiz 3 Mon 2023-03-22 (DC) [Mesh or Nodal]
Midterm Exam 1 Mon 2023-03-27 (DC) [Superposition , Thevenin, Norton, Mesh, Nodal]
Quiz 4 Mon 2023-04-05 (AC) [Superposition or Thevenin or Norton]
Quiz 5 Mon 2023-04-19 (AC) [Mesh or Nodal]
Midterm Exam 2 Mon 2023-05-01 (AC) [Superposition, Thevenin, Norton, Mesh, Nodal]
Quiz 6 Mon 2023-05-03 Polyphase (Delta-Star)

الحضور و الغياب:

  1. 1. الالتزام بالحضور وان لا يتعدى ١٢ ساعة غياب لتفادي الحرمان من المقرر.
  2. 2. كل غياب اربع ساعات سيترتب عليه خصم ٢٥٪ من درجة الغياب.
  3. 3. اي عذر طبي { رسمي من الجهات المختصة } يجب تسليمة قبل الغياب من المحاضرة ما عدى الحالات الطارئة.
  4. 4. لن يقبل اي عذر طبي لا يعوق دخولي على منصة تيمز.
  5. 5. الحضور سيسجل خلال اول عشر دقائق من بداية المحاضرة او من بداية انشاء الاجتماع للمحاضرة.

تسليم الواجبات والتقارير:

  1. 1. يجب تسليم الواجبات والتقارير حسب الشروط المطلوبة والموعد المحدد.
  2. 2. اي تاخير لتسليم الواجبات او التقارير سيترتب عليه خصم ٥٪ من الدرجة لكل ساعة تاخير عن الموعد.
  3. 3. يشترط ان تكون جميع الواجبات والتقارير المسلمة من عمل الطالب وادائه الشخصي فقط.
  4. 4. الاقتباس او النقل او الغش بالواجبات او التقارير المسلمة بما في ذلك شراء الواجبات او التقارير سيترتب عليه حرمان من النجاح في المقرر.

مسؤولية الطالب الادبية:

  1. 1. يتحمل الطالب كامل مسؤوليات ومتطلبات المقرر وان يعمل بجهد و اجتهاد لاجتياز المقرر بجدارة.
  2. 2. اجتياز المقرر او الرسوب فيه قد يحدد موعد التخرج.
  3. 3. كل ما سبق هو من مسؤولية الطالب الشخصية ويتحمل كامل اعبائها.

  1. Course presente by Dr. M. E. AlSharidah during spring of 2024 

2.2. Objectives

Course Objectives

  1. Analyze DC electric circuits using superposition theorem.

    1. Understand the difference between voltage and current sources when apply the theorem.
    2. Current and voltage sources transformation.
    3. Apply the superposition theorem in DC circuits.
    4. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  2. Analyze DC electric circuits using thevenin's theorem.

    1. Calculate Thevinens equivalent resistance.
    2. Calculate Thevinens equivalent voltage source.
    3. Apply Thevinens theorem to find the current and voltage at load.
    4. State the vale of load resistance for maximum power condition.
    5. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  3. Analyze DC electric circuits using mesh analysis.

    1. Write the mesh equations.
    2. Solve the mesh equations using matrix calculations.
    3. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  4. Analyze DC electric circuits using node analysis.

    1. Write the node equations.
    2. Solve the node equations using matrix calculations.
    3. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  5. Analyze AC electric circuits using superposition theorem.

    1. Understand the concepts of Fourier series and its application in circuit analysis.
    2. Compute the Fourier series for continuous-time periodic signals and apply frequency domain method of circuit analysis.
    3. Calculate rms value and harmonic content of a periodic waveform.
    4. Use computer simulation (Matlab and/or Pspice) tools to design and analyze simple circuits

  6. Analyze AC electric circuits using Thevenin's theorem.

    1. Calculate Thevinens equivalent impedance
    2. Identify the value of load impedance for maximum power condition.
    3. Calculate Thevinens equivalent voltage source.
    4. Apply Thevinens theorem to find the current and voltage at load.
    5. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  7. Analyze AC electric circuits using mesh analysis.

    1. Write the mesh equations.
    2. Solve the mesh equations using matrix calculations.
    3. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  8. Analyze AC electric circuits using node analysis.

    1. Write the mesh equations.
    2. Solve the mesh equations using matrix calculations.
    3. Use basic laboratory measurement equipment including the power supplies, digital multimeters, function generators, and oscilloscopes to conduct experiments.

  9. Recognize the basic voltages and currents relations in balanced three phase electric circuits.
    1. Recognize three phase electric circuits, Delta and Star connections
    2. Differentiate between the line and phase values
    3. Calculate the current in three phase balanced load, delta connection
    4. Calculate the current in three phase balanced load, star connection

2.3. Reference chapters:

The following selected chapters give in depth explanation on subjects related to the course.

3. Lectures and Labs

All course lecture and labs recorded meetings and notes

3.1. Lecture Notes

Lecture Notes

3.2. 70-115 lectures Channel

Mesh analysis example

Lectures and Labs on Microsoft Stream

4. Exam Examples

4.1. Example 1: Superposition

Using superposition, find the current through $R_1$

70-115-superposition-ex1

Simulation:

Using simulation as a guide, the circuit parameters will be as in the figue below.

70-115-superposition-ex1

Solution:

The solution is in two parts. First we turn the battery off and solve for the current in $R_1$. The second part, we turn off the current source and solve for the curent through $R_1$ due to the battery.


Step 1: I (ON) E (OFF)

e-off

Note that $R_3$ is shorted, and to obtain the current through $R_1$ we will use the current divider rule:

$$\begin{align}\text{Current divider rule: }\rightarrow I'_{R_1} &= \frac{R_2}{(R_1+R_2)}\cdot I \\
&=\frac{3.3 k\Omega}{(2.2 k\Omega + 3.3k\Omega)}\cdot 5mA \\
&=\frac{3.3 k\Omega}{5.5 k\Omega }\cdot 5mA \\
&=0.6\cdot 5mA \\
&=3mA \end{align}$$


Step 2: I (OFF) E (ON)

i-off

Since $R_3$ is in parallel with the battery, then the voltage across it is the battery voltage and it wont affect the current through $R_1$.
To solver for the current through $R_1$, we will only consider the resistances on the left side of the battery

$$\begin{align}\text{Ohm's Law: }\rightarrow I''_{R_1} &= \frac{E}{(R_1+R_2)}\\
&=\frac{8V}{(2.2 k\Omega + 3.3k\Omega)}\\
&=\frac{8V}{5.5 k\Omega }\\
&=1.455 mA \\
&=1.46 mA \end{align}$$


Step 3: Solving for $I_{R_1}$

$$\begin{align*}I_{R_1} &= I'_{R_1} + I''_{R_1} \\
&= 3 mA + 1.46 mA\\
&= 4.46 mA\end{align*}$$

4.2. Example 2: Superposition

Using superposition, find the voltage $V_2$ across the $6.8k\Omega$ resistor for the network of the figue below.

70-115-superposition-ex2

which is the same as

70-115-superposition-ex2-b

Simulation:

Using simulation as a guide, the circuit parameters will be as in the figue below.

70-115-superposition-ex2

Solution:

First we turn the battery off and solve for the voltage $V'_2$ across $R_2$. Then we turn off the current source $I$ and solve for the $V''_2$ due to the 36V battery.


Step 1: I (ON) E (OFF)

70-115-superposition-ex2-e-off

We can use the current divider rule to find the current through $R_2$ then use Ohm's law to find the voltage $V_2$:

$$\begin{align}\text{Current divider rule: }\rightarrow I'_{2} &= \frac{R_1}{(R_1+R_2)}\cdot I \\
&=\frac{12 k\Omega}{(12 k\Omega + 6.8k\Omega)}\cdot 9mA \\
&=\frac{12 k\Omega}{18.8 k\Omega }\cdot 9mA \\
&=0.638\cdot 9mA \\
&=5.745mA\\
\text{Ohm's law: }\rightarrow V'_2 &= R_2 \cdot I'_{2}\\
&=6.8k\Omega \cdot 5.75mA\\
&=(6.8\times 10^3) \cdot (5.75\times 10^{-3})\\
&= 39.06 V\end{align}$$


Step 2: I (OFF) E (ON)

70-115-superposition-ex2-i-off

which is equivalent to

70-115-superposition-ex2-i-off-2

Since $R_3$ is in parallel with the battery, then the voltage across it is the battery voltage and it wont affect the current through $R_1$.
To solver for the current through $R_1$, we will only consider the resistances on the left side of the battery

$$\begin{align}\text{Voltage divider rule: }\rightarrow V''_{2} &= \frac{R_2}{(R_1+R_2)}\cdot E\\
&=\frac{6.8 k\Omega}{(12 k\Omega + 6.8 k\Omega)} \cdot 36 V\\
&=\frac{6.8 k\Omega}{18.8 k\Omega } \cdot 36 V\\
&= 13.02 V \end{align}$$


Step 3: Solving for $V_2$

$$\begin{align*} V_2 &= V'_2 + V''_2 \\
&= 39.06 V + 13.02 V\\
&= 52.08 V \end{align*}$$

4.3. Example 3: Thevenin

Using Thevenin theorem, find the equivalent Thevenin circuit for the highlighted circuit from the a-b terminals.

70-115-examples-fig-00

Solving for $R_{TH}$

$$\begin{align}
R_{TH} &= R_1 + R_2 + R_3\\
&= 60\Omega + 20\Omega + 50\Omega \\
&= 130\Omega
\end{align}
$$


Solving for $E_{TH}$

$$\begin{align}
E_{TH} &= -E_1 -R_2\cdot I_2\\
&= -8V - (20\Omega) \cdot (150 mA)\\
&= -8V - 3V\\
&= -11V
\end{align}
$$

4.4. Example 4: Thevenin Theorem

Using Thevenin theorem, find the equivalent Thevenin circuit for the highlighted circuit external to $R_L$.

70-115-examples-fig-01

Solving for $R_{TH}$

$$\begin{align}
R_{TH} &= (R_1 //R_2) + R_3\\
&= \frac{10\Omega}{2} + 20\Omega \\
&= 25\Omega
\end{align}
$$


Solving for $E_{TH}$

$$\begin{align}
\text{Voltage divider rule:} \rightarrow E_{TH} &= \frac{R_2}{R_1+R_2} \cdot E_1\\
&= \frac{10\Omega}{(10+10)\Omega}\cdot 50V\\
&= \frac{10\Omega}{20\Omega}\cdot 50V\\
&= 25V
\end{align}
$$

4.5. Example 5: Norton

Using Norton theorem, find the equivalent Norton circuit for the highlighted circuit aross terminals a-b.

70-115-examples-fig-02

Solving for $R_{N}$

$$\begin{align}
R_{N} &= (R_1 //R_2) + R_3\\
&= \frac{(60\Omega) \cdot (30 \Omega)}{(60\Omega) + (30 \Omega)} + 25\Omega \\
&= 20\Omega + 25\Omega \\
&=45\Omega
\end{align}
$$


Using superposition to solve for $I_N$

$I'_N$: $E_1$ ON $E_2$ OFF

$$\begin{align}
\text{Solve for the voltage across $R_2$//$R_3$:} \rightarrow R_{23} &= \frac{R_2 \cdot R_3}{R_2 + R_3}\\
&= \frac{(30\Omega) \cdot (25\Omega)}{30\Omega + 25\Omega}\\
&= 13.64\Omega\\
\rightarrow V_{23} &= \frac{R_{23}}{R_1+R_{23}}\cdot E_1\\
&=\frac{13.64\Omega}{(60+13.64)\Omega}\cdot 15V\\
&=\frac{13.64}{73.64}\Omega\cdot 15V\\
&=2.778V\\
\therefore I'_N &= \frac{V_{23}}{R_3}\\
&=\frac{2.778V}{25\Omega}\\
&=111.1 mA
\end{align}
$$

$I''_N$: $E_1$ OFF $E_2$ ON

$$\begin{align}
\text{Solve for the total resistance:} \rightarrow R_{T} &= R_1 // R_2 + R_3\\
&=\frac{R_1 \cdot R_2}{R_1 + R_2}+R_3\\
&= \frac{(60\Omega) \cdot (30\Omega)}{60\Omega + 30\Omega}+25\Omega\\
&= 20\Omega+ 25\Omega\\
&=45\Omega\\
\therefore I''_N &= \frac{-E_{2}}{R_T}\\
&=\frac{-10V}{45\Omega}\\
&=-222.2 mA
\end{align}
$$

Solving for $I_N$

$$\begin{align}
I_N &= I'_N - I''_N\\
&=111.1mA - 222.2mA\\
&=-111.1 mA
\end{align}
$$

4.6. Example 6: Norton

Using Norton theorem, find the equivalent Norton circuit for the highlighted circuit aross terminals a-b.

70-115-examples-fig-03

Solving for $R_{N}$

$$\begin{align}
R_{N} &= R_1 //(R_2 + R_3)\\
&= \frac{(2.7k\Omega) \cdot (4.7k\Omega+3.9k\Omega)}{(2.7k\Omega) + (4.7k\Omega + 3.9k\Omega)} \\
&= \frac{(2.7) \cdot (8.6)}{11.3}k\Omega \\
&=2.055k\Omega
\end{align}
$$


Solving for $I_N$

$$\begin{align}
\text{Using current divider rule:} \rightarrow I_{N} &= \frac{R_3}{R_2 + R_3}\cdot I_s\\
&= \frac{3.9k\Omega}{4.7k\Omega + 3.9k\Omega}\cdot 18mA\\
&= 0.4535\cdot 18mA\\
&=8.163mA
\end{align}
$$

4.7. Example 7: Mesh Analysis

Using Norton theorem, find the equivalent Norton circuit for the highlighted circuit aross terminals a-b.

70-115-examples-fig-04

Solving for mesh currents using calculator

70-115-mesh-ex7

4.8. Example 8: Mesh Analysis

Using Norton theorem, find the equivalent Norton circuit for the highlighted circuit aross terminals a-b.

70-115-examples-fig-05

Solving for mesh currents using calculator

70-115-mesh-ex8