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How do you relate AC and DC voltage by means of complex numbers?
Wiki User
∙ 11y ago
A complex number is a combination of real and imaginary numbers. An example of a complex number is the expression (a + jb), in which the letter j is called an 'operator'. In this example, the operator +j indicates that the quantity b is acting at an angle of +90o to quantity a -or is 'leading' a by 90o. If the operator was -j, then it would be indicating that quantity bis acting at -90o to quantity a -or is 'lagging' a by 90o.
Mathematicians use the letter 'i' to represent an imaginary number, but in electrical engineering we use the letter 'j'. This is because we already use a lower-case 'i'to represent an instantaneous value of current. In mathematics, the operator is sometimes written after the quantity to which it applies (i.e. 'bj'), but it is more usual, in engineering, to place the operator in front of that quantity (i.e. 'jb').
The application of the operator 'j' to a phasor, then, acts to rotate that phasor, counterclockwise, through 90 degrees.
The term, 'imaginary', is misleading -it doesn't mean that it exists only in the mind! It is simply a mathematician's term for 'quadrature', meaning 'lying along the y-axis'.
A.C. quantities, such as current and voltage, can be resolved into horizontal and vertical components. So, we can represent an alternating-current quantity by a complex number which represents its in-phase component together with its quadrature (plus or minus 90o) component. For example, 3+j4 could represent a 5-A current, whose in-phase component is 3 A, and whose quadrature component is 4 A (i.e. which leads the in-phase component by 90o).
Complex numbers enable complex a.c. circuits to be resolved relatively easily, and without the need to construct complicated phasor diagrams.
As in-phase and quadrature ('imaginary') components only apply to a.c. quantities, we do not need to apply complex numbers to d.c.
Wiki User
∙ 11y ago
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What is sending voltage?
sending voltage means voltage applied to source side.....
What is the definition of complex definition in technical writing?
complex definition in tecnical writing means the word which is complex to define.
How many dB attenuation translates into 75 percent of voltage being lost to attenuation?
100 percent means full voltage or 0 dB.When 75 percent of the voltage is lost you still have 25 percent of the voltage.25 percent means damped to (-)12 dB.
How the voltage circuit work?
i.e normally we have various sensors to measure the voltage but my doubt is, how the voltage circuit measures the voltage i.e i need the detail for each and every unit.... If anybody know means plz tell to me.....
What is The meaning of Voltage 'V ab' is the voltage at?
V ab is the voltage between two nodes of the circuit. See also Kirchoff's Voltage Law. WHILE CORRECT IT REALY MEANS POINT a to point b in a circuit.
Why complex numbers used in impedance?
Because there is an angle involved. If - for example - the resistance (the real part) is 10 ohms, and the reactance (the imaginary part) is also 10, then there is an angle of 45 degrees; which actually means that this will be the displacement angle between the voltage and the current.Impedance may just be specified with an angle; but it turns out that the calculations between voltage, current, and impedance correspond precisely to the calculations with complex numbers.Because there is an angle involved. If - for example - the resistance (the real part) is 10 ohms, and the reactance (the imaginary part) is also 10, then there is an angle of 45 degrees; which actually means that this will be the displacement angle between the voltage and the current.Impedance may just be specified with an angle; but it turns out that the calculations between voltage, current, and impedance correspond precisely to the calculations with complex numbers.Because there is an angle involved. If - for example - the resistance (the real part) is 10 ohms, and the reactance (the imaginary part) is also 10, then there is an angle of 45 degrees; which actually means that this will be the displacement angle between the voltage and the current.Impedance may just be specified with an angle; but it turns out that the calculations between voltage, current, and impedance correspond precisely to the calculations with complex numbers.Because there is an angle involved. If - for example - the resistance (the real part) is 10 ohms, and the reactance (the imaginary part) is also 10, then there is an angle of 45 degrees; which actually means that this will be the displacement angle between the voltage and the current.Impedance may just be specified with an angle; but it turns out that the calculations between voltage, current, and impedance correspond precisely to the calculations with complex numbers.
What do imaginary numbers represent?
The real numbers together with the imaginary numbers form a sort of vector. What these complex numbers (complex means the combination of real and imaginary numbers) represent depends on the specific situation. Just as there are situations where it doesn't make sense to use negative numbers, or fractional numbers, in many common situations it doesn't make sense to use complex numbers. In an electrical circuit (specifically, AC), the real numbers might represent resistance, while the imaginary number represent reactance - and voltages and currents are also represented by complex numbers, with the angle of the complex number representing how much one quantity is ahead or behind another quantity (the "phase angle"). In quantum mechanics, the complex numbers might not represent anything (perhaps they don't, I am not sure...), but they are useful for calculations.
Is one a real complex pure imaginary or nonreal complex number?
One is a complex number and a real number.
Is 2 and a half a complex number number?
2 ½ is called a mixed number (a whole number and a fraction), not complex.Complex number means there can be real and/or imaginary parts to a number. Without confusing you though, complex numbers include all of the real numbers (which include all fractions and mixed numbers).
What is sending voltage?
sending voltage means voltage applied to source side.....
What is an algebra word that start with the letter a?
associative Abelian (named after Abel, and means commutative) Argand diagram (in complex numbers) Asymptote (asymptotic)
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
What are two numbers that have the product of 30 and the sum of 9?
According to Wolfram Alpha, (1/2) (9 plus or minus i times the square root of 39) Since these numbers are complex, it means there is no solution with real numbers for this problem.
How are imaginary numbers used in electricity?
The very simplified answer is that imaginary numbers put together with real numbers (to make a complex number) can describe the timing of voltage relative to current, or current relative to voltage, in an AC circuit. Let's say that we're driving an AC electrical circuit with an oscillating current source, and measuring a resulting oscillating voltage. Here's the rub:Purely Real: If you put a resistor in the circuit and measure the voltage oscillations across it, the voltage will be a purely real number. This means that the timing of the voltage peaks will match the timing of the current peaks exactly.Purely Positive Imaginary: Now, put an inductor in the circuit instead of a resistor and measure the voltage oscillations. It will be a purely positive imaginary voltage. This does not mean that the voltage is non-existent (as many people think)! It simply means that the voltage peaks will be one quarter cycle ahead of the current peaks, or 90 degrees ahead. The voltage has physical value. If you were to touch the ends of the inductor, you would still get shocked! The imaginary property just tells you that the timing is ahead by a quarter cycle, that's all--nothing esoteric or "complicated." A good analogy to this would be if you were riding your bicycle side by side with your friend, and you were pedaling at the same rate, BUT your pedal was consistently a quarter turn ahead of his.. Your timing could be considered purely imaginary relative to him (or her).Purely Negative Imaginary: Now, put a capacitor in the circuit and measure the voltage oscillations. It will be a purely negative imaginary voltage, which simply means that the voltage peaks will be one quarter cycle behind of the current peaks, or 90 degrees lagging.Complex: By putting a combination of resistors, inductors, and capacitors in the circuit together, you get a complex voltage, allowing you to get "in between" values. For example, you could carefully size a resistor and inductor, put them in series, and force the voltage peaks to be 45 degrees ahead.Hope this is clear. If it's still cloudy, I'll paste a link in the web link area that has a site out there with an interactive explanation showing how imaginary numbers can be used with complex numbers to represent both size and timing (it's actually my site, but for educational purposes only).While these answers mainly deal with electric power [alternating current], the same concepts apply to waves in general which have a phase difference [difference in timing of peaks and valleys of the waves].Please see the below link for a graph of the fields around current carryingconductors by the formula: w=(z-1)/(z+1), z=x + iy.
What are the math teritories?
Well, I think that means differnet types of math fields. This would mean like arthmitic, equations, complex numbers and so on.
What is the definition of a complex institution?
I think Complex Institution means the religion background ..
What is DC in voltage means?
This means direct current.
