With hydroelectric power, water flowing through turbines turn generators. Generators produce alternating voltages due to the circular motion of the components around a shaft. The voltage produced changes through the rotational cycle as the angle between the fixed components and the rotating components changes, and is perfectly described by the sine wave.
The speed of the rotation determines the frequency of the wave. This is where the mechanical motion, the mathematics, and the voltages are tied together. Power transmission requires high voltages to cover long distances. At very high voltages, huge amounts of power can travel at manageable currents, so the wires can be or reasonable size. However these very high transmission voltages are incredibly hazardous and would be impossible for end user use. Transformers make it possible to step alternating voltages up and down.
The output of turbines can be increased or "stepped up" for transmission, then decreased or "stepped down" by transformers at substations for local distribution, then stepped down again by utility transformers near subscribers for end use.
So the existence of transformers for AC are what make AC suitable for production in power plants, transmission to substations, and distribution to power company customers far from the original source. So at the most basic level, the sinusoidal voltage curve seen on an oscilloscope at a receptacle in your house is directly tied to the rotation of a generator back at a power plant.
Obviously a major oversimplification of the modern power grid, your power doesn't trace back to a single generator at a single power plant While alternating currents produced by rotating machinery will naturally be produced in a sinusoidal wave, AC is not defined as sinusoidal; it is entirely possible to generate other non-sinusoidal alternating currents.
The sine wave is a consequence of the way the AC is produced. When driving a generator you simply cannot directly create DC. Further it's may important to notice that the electrons are not moving like a mass connected to a spring.
If current is positive they move in one if current is negative they move in the other direction, but not representing any sinusoidal motion. The sinusoidal current comes from the amount of electrons - this just as a sidenote. One of the reasons we mainly use AC is due to the fact of easy transformation. In the early really early beginning everything started with DC, but when transmitting DC the losses are way higher then with high voltage AC.
The sinusoidal waveform is by design. The sinusoidal waveform and use of three phases allows the electricty to drive induction motors which being brushless are very durable and quiet running.
You do get something simple harminic motion in radio antennas, but power transmission lines are balanced so the induction and capacitance effects seen in antennas aren'r present to the same extent. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?
Learn more. Why 'sine' wave of alternating current? Ask Question. Asked 3 years ago. Active 3 years ago. Viewed 4k times. The Dude. The Dude The Dude 1 1 1 silver badge 2 2 bronze badges. Also at each stage of transformation the waveform would slowly approach a perfect sine wave due to the filtering nature of these losses.
So one just sticks to the sine wave as generated by your rotating machine. The capacitor blocks the DC produced by the diode. The capacitor is in series. But for DC conversion, the capacitor has to be in parallel with the resistor. Add a comment. Active Oldest Votes. That's the whole difference between D. Source That's a very vague question. If you're talking about a graph of a D. Factors" by definition. The only thing I can think your teacher may be referring to is perhaps noise, which is in fact alternating, and can appear like "A.
Given the current or voltage as a function of time, we can take the root mean square over time to report the average quantities. The root mean square abbreviated RMS or rms , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when the function alternates between positive and negative values, e.
The RMS value of a set of values or a continuous-time function such as a sinusoid is the square root of the arithmetic mean of the squares of the original values or the square of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a series of equally spaced samples.
Sinusoidal Voltage and Current : a DC voltage and current are constant in time, once the current is established. The voltage and current are sinusoidal and are in phase for a simple resistance circuit. The frequencies and peak voltages of AC sources differ greatly. V is the voltage at time t , V 0 is the peak voltage, and f is the frequency in hertz. First, we have. Since V 0 is a constant, we can factor it out of the square root, and use a trig identity to replace the squared sine function.
Since the interval is a whole number of complete cycles per definition of RMS , the terms will cancel out, leaving:. Many of the equations we derived for DC current apply equally to AC. If we are concerned with the time averaged result and the relevant variables are expressed as their rms values. We can see from the above equations that we can express the average power as a function of the peak voltage and current in the case of sinusoidally varying current and voltage :.
Average Power : AC power as a function of time. Since the voltage and current are in phase here, their product is non-negative and fluctuates between zero and I0V0. The RMS values are also useful if the voltage varies by some waveform other than sinusoids, such as with a square, triangular or sawtooth waves.
Waveforms : Sine, square, triangle, and sawtooth waveforms. Electrical safety systems and devices are designed and widely used to reduce the risks of thermal and shock hazards. Identify major risks associated with the electrical circuits and strategies to mitigate those risks.
Electricity has two hazards. A thermal hazard occurs in cases of electrical overheating. A shock hazard occurs when an electric current passes through a person.
There are many systems and devices that prevent electrical hazards. It lacks safety features. In practice, a simple AC circuit with no safety features is not how power is distributed. Modern household and industrial wiring requires the three-wire system, which has several safety features. The first safety feature is the familiar circuit breaker or fuse that prevents thermal overload. Secondly, there is a protective case around the appliance, as with a toaster or refrigerator.
The case prevents people from touching exposed wires and coming into electrical contact with the circuit, helping prevent shocks. Three-Wire System : The three-wire system connects the neutral wire to the earth at the voltage source and the user location.
It exists at zero volts and supplies an alternative return path for the current through the earth. The case of the appliance is also grounded to zero volts. Wire insulation colors vary by region.
It is essential to check locally to determine which color codes are in use, even if they were followed in one particular installation. This wire is therefore safe to touch even if its insulation is missing. The neutral wire is the return path for the current to follow in order to complete the circuit.
The three-wire system is connected to an appliance through a three-prong plug. Three-Prong Plug : The standard three-prong plug can only be inserted one way to ensure the proper function of the three-wire system.
Grounding the case solves more than one problem, however. Some appliances are still sold with two-prong plugs. Neutral wires may be blue, black, or white.
Electromagnetic induction causes a subtler problem solved by grounding the case. The alternating current in appliances can induce an EMF on the case. If grounded, the case voltage is kept near zero, but if the case is not grounded, a shock can occur. Current that is driven by the induced case EMF is called a leakage current, although current does not necessarily pass from the resistor to the case.
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