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A power-line carrying a sinusoidal AC voltage with maximum of 325 V is traveling across the city. What is the DC voltage of equivalent power? | A power-line carrying a sinusoidal AC voltage with maximum of 325 V is traveling across the city. What is the DC voltage of equivalent power? | ||
<math>\Delta V_{rms} = {\sqrt{\frac{1}{2}}} \Delta V_{max}</math> | |||
With <math>V_{max}</math> 325 V, the DC voltage of equivalent power <math>325V* \sqrt{\frac{1}{2}}</math> which is approximately 230 V. | With <math>V_{max}</math> 325 V, the DC voltage of equivalent power <math>325V* \sqrt{\frac{1}{2}}</math> which is approximately 230 V. | ||
Revision as of 22:25, 1 December 2015
This topic covers AC (Alternating Current). Claimed by bwalker60
The Main Idea
Alternating current is a varying current driven by varying voltages. This means the current is constantly changing (in both magnitude and direction) as a function of time. This is opposed by Direct Current, in which the current is constant and non-varying in either direction or magnitude.
Alternating current powers most appliances in residential and commercial areas. The wall outlets found in homes are connected to alternating current circuits. Alternating current is the predominant power source for most residential areas in order to efficiently and easily convert high AC voltages (straight from the power plant) to lower AC voltages (used in residential areas by appliances). Until recently, conversion from high DC voltages to low DC voltages was quite difficult and inefficient.
Alternating current is typically found in a sine wave function pattern. In the U.S, the standard power-line frequency is 60 hertz, meaning the AC voltage oscillates completely 60 times per second. In most European countries the standard power-line frequency is 50 hertz.
AC Power
An AC circuit that varies in a sine waveform between -155 V and +155 V is called a "110 volts AC" circuit because it delivers the same amount of energy in one second as a constant (DC) circuit at 110 V. This is an example that the average power of an AC circuit is less than the power of an equivalent maximum voltage DC circuit.
Phase Shift
In an AC circuit the current does not need to be in phase with the voltage, meaning the current and voltage of the circuit do not necessarily peak or reach their maximum/minimum values at the same time. If the voltage peaks later than the current in an AC circuit it is said that the current in the circuit "leads" the applied voltage.
A Mathematical Model
Root Means Square Voltage
[math]\displaystyle{ \Delta V_{rms} }[/math] is the Root Means Square voltage of an AC circuit. This represents the voltage at which a DC circuit would produce the same power as the AC circuit with voltage [math]\displaystyle{ V_{rms} }[/math]
RMS Voltage For a Sinusoidal AC circuit:
[math]\displaystyle{ \Delta V_{rms} = {\sqrt{\frac{1}{2}}} \Delta V_{max} }[/math]
Average Power
[math]\displaystyle{ P_{avg} }[/math] is the average power an AC circuit can produce with a given Root Means Square Voltage.
[math]\displaystyle{ P_{avg} = {\frac{\Delta V_{rms}^2}{R}} }[/math]
Phase Angle
[math]\displaystyle{ \phi }[/math] represents the Phase Angle of an AC circuit which is the offset value causing the Phase Shift between applied voltage and current in a sinusoidal AC circuit.
[math]\displaystyle{ \tan( \phi) = {\frac{1}{RC \omega}} }[/math]
Max Current
This represents the maximum current an AC circuit can achieve given the maximum applied Voltage.
[math]\displaystyle{ I_{max} = \frac{\Delta V_{max}}{\sqrt{R^2 + \frac{1}{(C \omega)^2}}} }[/math]
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
A power-line carrying a sinusoidal AC voltage with maximum of 325 V is traveling across the city. What is the DC voltage of equivalent power?
[math]\displaystyle{ \Delta V_{rms} = {\sqrt{\frac{1}{2}}} \Delta V_{max} }[/math]
With [math]\displaystyle{ V_{max} }[/math] 325 V, the DC voltage of equivalent power [math]\displaystyle{ 325V* \sqrt{\frac{1}{2}} }[/math] which is approximately 230 V.
Middling
Difficult
Connectedness
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- How is it connected to your major?
- Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
See also
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Further reading
Books, Articles or other print media on this topic
External links
Internet resources on this topic
http://www.allaboutcircuits.com/textbook/alternating-current/#chpt-1
https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/alternating-current-1
References
This section contains the the references you used while writing this page
Chabay, Ruth W., and Bruce A. Sherwood. "Ch 19 Section 9: "*What Are AC and DC?"" Matter & Interactions. Electric and Magnetic Interactions. Hoboken, NJ: Wiley, 2011. N. pag. Print.
"Vol. II - Alternating Current (AC)." - Electronics Textbook. N.p., n.d. Web. 01 Dec. 2015. <http://www.allaboutcircuits.com/textbook/alternating-current/#chpt-1>.
"Alternating Current - MagLab." Alternating Current - MagLab. N.p., n.d. Web. 01 Dec. 2015. <https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/alternating-current-1>
Whelan, M., Joseph Cunningham, and S. Rockwell. "AC Power History and Timeline." AC Power History. Edison Tech Center, n.d. Web. 01 Dec. 2015. <http://www.edisontechcenter.org/AC-PowerHistory.html>.