Electricity and electrical components are a major part of our lives today. Our lives pretty much come to a halt if there is a power outage or if our electrical devices stop working, sometimes we even start panicking because we are so dependent on these components that we cannot afford to lose them and their importance and use only increases as time passes. We all use these electrical devices and also electricity itself but most of us do not think about the math and physics that works behind all of these things.
In this paper, I will talk about how AC circuits can be described by considering voltage and current using complex numbers. An AC circuit requires two separate numbers to be able to completely describe it. This is because it takes into account the amplitude and the phase of the current. The fact that complex numbers can be easily added, subtracted, multiplied or divided with each other makes them ideal for this operation where both amplitude and phase have to work together.
For a DC circuit, Ohm’s Law is used. According to the Ohm’s law, v=iR Where, v= voltage i= current flowing through the circuit
R= resistance offered by the resistors attached in the circuit.
Whereas, there is an AC analogy for the Ohm’s that is used. Here, the equation for the Ohm’s law changes to: v=iZ Where, v= voltage i= current flowing through the circuit
Z= impedance
Here, all the three quantities can be used as complex numbers. Z defines a quantity called impedance. Impedance acts in a similar way as resistance in a DC circuit. Also, if the frequency of the AC circuit is allowed to go to 0, impedance will go down to 0 as the imaginary part of it will disappear, hence, making it equal to the resistance in a DC circuit.
In the paper, the followi...
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...he original vector.
P*=A-jB
The modulus of a complex number is the square root of the sum of squares of each real and imaginary part of the number. It is denoted by |P| if P is the complex number.
|P|=√(A^2+B^2 )
A complex number may also be expressed in a polar form using the Euler’s Formula:
P=A+jB=exp(jθ)=cosθ+jsinθ
Also,
P=|P|exp(jθ)
And tanθ=B/A Relation of the AC Circuit and Complex numbers
Complex numbers provide a structure to describe sinusoidal functions of time, especially the current and voltage functions that are observed in AC circuits.
The exponential for of the complex numbers is the most useful because the relationship between voltage and current is about multiples. In sinusoidal voltages, different types of impedances/resistances exist. Here, I am particularly talking about capacitors and inductors, excluding the non-linear devices.
The reason I will test my theory is so I can see if ohm's law was
I therefore predict that the higher the intensity, the greater the emf across the cell, the greater the power output of the
Mesh analysis is a method that is used to solve planar circuits for the voltage and currents at any place in the circuit. Mesh analysis uses Kirchhoff’s voltage (and current) laws to understand and solve these planar circuits. Mesh analysis is a systematic approach for solving planar circuits and reduces the number of equations needed to solve the circuit for all of the voltages and currents. Similar methods exist such as the Branch Current method which is similar in its style using Kirchhoff’s and Ohm’s laws.
In this paper, I will examine fundamental elements of a conductor’s relationship
I am writing this essay to explain to you what is going on in the circuit that was given to me. I will explain with the best of my knowledge so that you can fully understand what is happening in the circuit. The inductor and the wires are assumed as being ideal. The AC voltage source has an infinitely variable frequency (0≤f≤∞). The values of all the resistors, capacitor, and inductor are constant.
r = 4a cos^3 (q/3). For the specific equation for the graph, the polar form is the equation of greatest ease of use. Use 1 in place of “a” and switch the calculator to polar form. The best viewing window for this graph is q min= -360; q max= 360; q step= 10; x-min= -5; x-max= 5; x scale= 1; y-min= -5; y-max= 5; y scale= 1. This window and equation will give an excellent picture of the curve, Cayley’s Sextic.
!) You have two circuits: one is in parallel and the other is in series. Both circuits each contain a 6 resistor, and a 10 resistor, however the parallel circuit also has an additional 12 resistor in parallel. Which of these statements is true about the total resistance of the
imaginary. Over the centuries the letter “i” was still used in equations therefore, the name
where I is the current through the conductor in units of amperes, V is the potential difference
V(voltage) I (current) Therefore, I = V R Therefore, if V is constant, in order to increase I, R must decrease.
(Pavelka and Čeřovský, 2002). Rectifiers convert an input AC voltage and current to an output DC voltage and current, choppers convert an input DC voltage and current to an output DC voltage and current of different values, inverters convert an input DC voltage and current to an output AC voltage, current, frequency and count of phases, AC converters convert an input voltage, current, count of phases and frequency to an AC energy with different parameters. The frequency converters that convert an input frequency to an output frequency and that simultaneously maintain the count of phases create a subgroup of AC converters
As an engineering student, design, develop and test electrical equipments is the major purpose of all time. In other words, electrical engineer is concerned with using electricity to transmit electric power. In electrical engineering, there are extensive subfields such as power engineering, control system and signal processing. It is also worth to point out the difference between electrical engineering and electronic engineering. According to the research, electronic engineering is a major that deal with the electronic system such as computers and radar, to be more specific, electronic engineers are concerned with using electricity to process information.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology.Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of hyperbolic
The effects of electricity control much of our daily lives. Many of our gadgets and everyday tasks are run by this wonderful source of power. For example without electricity we would not be able to make a cup of coffee in the mourning, or even make a long distance call to family or friends. There have been several technological breakthroughs by many brilliant people throughout history regarding electricity. It has come from being discovered as a small current to being transformed into useful power to run such things as computers. Ben Franklin, Guglielmo Marconi, Thomas Edison, Paul Nipkow, and Charles Babbage have all contributed to the advancement of electricity, and all of their advancements have supplied society in many ways.
With reference to Eq. (1), ∆V/∆T refers to the rate of fluid volume flow, while A refers to the cross-sectional area and V the fluid velocity at points 1 and 2 in a tube respectively. From Eq. (1), it can be seen that as the rate of fluid volume flow is assumed to be constant for an incompressible fluid, a decrease in the cross-sectional area of a tube would lead to an increase in the fluid velocity passing through it3.