Engineering problems Essay Example

Introduction

The general engineering study entails understanding challenges in different fields of study especially in the field of mathematics and other sciences like physics. Understanding these subjects helps an engineering student in tackling some of the challenges that they may face in future. Application of theoretical formulas learned in class to get the required results as shown in this essay has been used to show that the students understand the theories learned in class and can be able to apply them in solving various tasks. Below is a summary of the test areas in the exercise:

Task 1(a)

• Electrical systems
• Circuits
• Phase angle interpretations (Impedance and current).
• What is Power Factor and how to maximize its results?

Task 1(b)

• Roof structure framework
• The Argand diagram
• Magnitude of members
• Direction of forces in roof members
• Analyses of the solved solution

Task 2(a)

• Newton- Raphson procedure

Task 2(b)

• Numbering system
• Converting a number to binary via octal
• Steps of converting:
• Decimal to Octal
• Octal to Binary

Task 2(c)

• Logic systems
• Logic circuit
• Achieving a NAND only gate.

Task 2(d)

• De-Moivre’s Theorem
• Using the theorem in calculations in both polar and Cartesian coordinates

The above test will be achieved through definitions of the various topics and discussions of the calculated values of the examples in the tasks.

Discussion

Electrical systems

Electrical systems can be defined as full electrical systems or sub-systems that contain a group or groups of electrical components. The success of these systems is fully dependent on the design and choice of the components in the system. These systems are comprised of electrical circuits that are meant to complete certain tasks when their operations are completed. Electrical systems studies are comprised of the fundamental mathematics of electrical signals, information technologies and the physical science of the electrical phenomena.

Circuits

As mentioned earlier, electrical systems comprise of circuits. These circuits are defined as paths that are followed by electrons emanating from a voltage or a current source.

As a component of the electric circuit, the electric current can be defined as a flow of electric charge.

Phase angle

During transmissions of alternating current, capacitors and inductors in a circuit tend to reach peak levels at different times. The difference in the peaks regarding degrees is called phase angle and is usually 90⁰.

Impedance

Impedance is represented by the symbol (Z) in the electrical calculation, and it is defined as the resistance that is applied a current of a system when a voltage is introduced. From the definition, impedance is as a result of dividing the voltage value with the current value. From the voltage and current graphs, impedance is the difference between the current and voltage curves. The answer for the impedance from the exercise is 591.04⁰ /-32.22 ohms, a value that is approximately the same as the calculated value through the formula:

Z= √{R² + (X_L-X_C)²}

Whereby:

R is the overall value of the resistance and X_L, X_C is reactance across the inductor and capacitor respectively.

The current is also calculated by dividing the input voltage with the total resistance of the circuit to get a value of 32.22 ohms. The results indicate that the impedance of the system is equal to the current value of the system.

Power factor

Power factor could be described as the ratio of the actual power flowing in an AC circuit to the product of root mean square values of the current and voltage in the circuit. The ideal value for power value is 1 and does not have units since it is a ratio. The perfect value of one is only achievable by re-arranging the capacitance and inductance formulas in such a way that the capacitance and reactance are made to vary while the inductance remains the same.

Roof structure framework

A roof structure framework allows for the interconnection of roof members to create a stable roof structure. The framework takes care of forces and direction of forces in the roof members.

Argand diagram

This is a diagram on which complex numbers are represented geometrically using Cartesian and polar coordinate systems. This diagram has been used in the exercise to show the amount of the forces affecting the members and their direction graphically. By the help of calculations, the amount of force in action for the members is a positive 1285 kN acting in a negative direction of 74.69⁰. Negative directions are shown by putting a negative sign in front of the directional value. In this case, the direction is written as -74.69⁰. The negative values mean that the forces act away from the joint of members and the negative values is found on the left-hand side of the x-axis and the lower part of the y-axis of the Argand diagram. The rest of the parts of the diagram show positive values.

Newton-Raphson procedure

The Newton-Raphson procedure is a scientific method of analysis that was discovered by Isaac Newton and Joseph Raphson. It is a procedure that is used in finding most appropriate approximations of roots of real-valued functions. It is commonly used in the analysis of thermodynamic functions. Given the first estimations of the values, the procedure is then used to find the rest of the estimate values of the data. The second (r) value of the data is derived from the first R-value by application of the procedure, and the answer 0.171 was found through the formula (x₁-f(x₁)/f’(r₁)) then the answer rounded off to three decimal places.

Number system

This is a way of representing numbers using different bases. In the exercise, the octal and binary numbers are in base eight and two respectively. The exercise requires of a decimal number to octal first then finally to binary. The two whole part of the number is treated differently from the part with a decimal value. In the exercise, the whole number part is multiplied by eight and the decimal part multiplied by six to make two values of 4 and six respectively. The numbers are then changed to binary by changing each octal number into three digits which give 100 for digit 4 and 110 for digit six hence the binary number becomes 100110.

Logic gates.

A logic gate in electronics is an idealized device that implements the Boolean function. There are seven different types of gates though some are as a result of a combination of other gates. The gates are namely: AND, OR, NOT, NAND, NOR EXOR and EXNOR gates. In the exercise, a logic function is created using AND, OR and NAND to give a simplified logic system.

De-Moivre’s theorem

De-Moivre’s theorem is a direct method of finding solutions to complex numbers in mathematics. In the exercise, the theorem has been used to calculate the results of Z2= 32( √3+j) which includes a complex number. The answer was then compared with one from the Argand diagram to test for accuracy.

Conclusion

Mathematical concepts learned in class are put into test through calculation of sample exercises. Some of the concepts learned in class are as listed in the introduction summary. Their applications in calculating different sample exercises prove understanding of the concepts studied.

References

Singh, J., 2008. Modern physics for engineers. John Wiley & Sons.

Kreyszig, E., Kreyszig, E. and Norminton, E.J., 2006. Advanced engineering mathematics (Vol. 72). New York: John Wiley.

Kaplan, S.M., 2004. Wiley Electrical and Electronics Engineering Dictionary. Wiley-Interscience.