Circuit Theory/Phasor Analysis Phasor Analysis[edit] The mathematical representations of individual circuit elements can be converted into phasor notation, and then the circuit can be solved using phasors. Resistance, Impedance and Admittance[edit] In phasor notation, resistance, capacitance, and inductance can all be lumped together into a single term called "impedance". The phasor used for impedance is . is Voltage and is current. And the Ohm's law for phasors becomes: It is important to note at this point that Ohm's Law still holds true even when we switch from the time domain to the phasor domain. Impedance is still measured in units of Ohms, and admittance (like Conductance, its DC-counterpart) is still measured in units of Siemens. Let's take a closer look at this equation: If we break this up into polar notation, we get the following result: Resistors[edit] Resistors do not affect the phase of the voltage or current, only the magnitude. Capacitors[edit] A capacitor with a capacitance of C has a phasor value: Where
Phasor An example of series RLC circuit and respective phasor diagram for a specific Glossing over some mathematical details, the phasor transform can also be seen as a particular case of the Laplace transform, which additionally can be used to (simultaneously) derive the transient response of an RLC circuit.[10][8] However, the Laplace transform is mathematically more difficult to apply and the effort may be unjustified if only steady state analysis is required.[10] Definition[edit] Euler's formula indicates that sinusoids can be represented mathematically as the sum of two complex-valued functions: [a] or as the real part of one of the functions: The term phasor can refer to either [citation needed] or just the complex constant, . An even more compact shorthand is angle notation: See also vector notation. A phasor can be considered a vector rotating about the origin in a complex plane. . represents the angle that the vector forms with the real axis at t = 0. Phasor arithmetic[edit] In electronics, and .
AC power The blinking of non-incandescent city lights is shown in this motion-blurred long exposure. The AC nature of the mains power is revealed by the dashed appearance of the traces of moving lights. Real, reactive, and apparent power[edit] In a simple alternating current (AC) circuit consisting of a source and a linear load, both the current and voltage are sinusoidal. If the load is purely resistive, the two quantities reverse their polarity at the same time. If the loads are purely reactive, then the voltage and current are 90 degrees out of phase. Practical loads have resistance, inductance, and capacitance, so both real and reactive power will flow to real loads. Engineers care about apparent power, because even though the current associated with reactive power does no work at the load, it heats the wires, wasting energy. Conventionally, capacitors are considered to generate reactive power and inductors to consume it. The complex power is the vector sum of real and reactive power. .
What is reactive power Reactive power is an odd topic in AC (Alternating Current) power systems, and it's usually explained with vector mathematics or phase-shift sinewave graphs. However, a non-math verbal explanation is possible. Note that Reactive power only becomes important when an "electrical load" or a home appliance contains coils or capacitors. If the electrical load behaves purely as a resistor, (such as a heater or incandescent bulb for example,) then the device consumes "real power" only. Reactive power is simply this: when a coil or capacitor is connected to an AC power supply, the coil or capacitor stores electrical energy during one-fourth of an AC cycle. In other words, if your electrical appliance contains inductance or capacitance, then electrical energy will periodically return to the power plant, and it will flow back and forth across the power lines. This undesired "energy sloshing" effect can be eliminated. Why is reactive power so confusing? What is imaginary power? What is real power?
Reactive power The first place you should look is search for 'reactive power'. There are contributors to this site who will insist that reactive power doesn't "flow", or that there's no such thing as reactive "power". But for the purposes of this contribution (and per commonly acepted convention--see we will consider that reactive power does indeed exist and that it flows. And remember: the originator of this thread asked for an explanation in layman's terms, which for me, anyway, does not initially include vector diagrams and trigonometry and mathematical formulae. All of these things are necessary for a complete and proper understanding of the phenomenon, but not for a rudimentary understanding on which to base all of the formulae and vector diagrams, etc., which just serve as mathematical proofs of the principles. In an AC power system, there are resistive loads and reactive loads. Okay, a hot, flat beer is worse.
reactive power Question I also faced this Question!! Rank Answer Posted By Re: wat is the importance of reactive power in power generation.....if it is zero means wat will happen to system........ AC power can be classified in to active power and reactive power. importance of reactive powers are to Maintain and control the voltage balance on the system, Avoid damage to the Transmission System, Generation plant and Other connected parties• The provision of Reactive Power by all Generation Units for voltage support is vital to maintain a secure and stable Transmission System. dear gobi.........if reactive power zero means p.f will increase...ok...at that time voltage will rise r not....this will not affect the transmission?.... if reactive power of generator is zero. required reactive power is drawn from the grid or other generators. [Century Cement Baikunth] Inadequate reactive support ! wat is the limit for that reactive power? Asked @ Answers What are the difference between C-Curve and D-Curve for MCB's. Essar
What is meant by Active and reactive power? Question I also faced this Question!! Rank Answer Posted By Re: What is meant by Active and reactive power? working power ( KW )to perform the actual work of creating heat ,light,motin,etc reactive power ( KVAR ) to sustained the magnetic field it does not work ( Loss ) Active power is nothing but the actual power ( Kw ) or Real power Consumed by a load .If we are not maintaining the power factor at the appreciable value that is if cos0 is decreasing then sino is increased that is VI SIN o is reactive power. cos o = Active power / Apparent Power = Kw / KVA Reactive power = VI SINo = Kvar. kVA is apparent power(S), it consist of Reactive power (Q in var volt ampere reactive)(for building electric and magnetic fields) and Active power (P in W watts))(working power- for heating, rotating machines,etc ) it is also thru that S² = P² + Q² . active power is the actual usefulmpower, reactive power means inductive power which increase means we have to improve power factor for balancing the system Ecil
Generalized Ohm's Law and Impedance Next: Impedance and Generalized Ohm's Up: Chapter 3: AC Circuit Previous: Sinusoidal Functions In the following discussion about AC circuit analysis, all sinusoidal variables (currents and voltages) are assumed to be of the same frequency. In general, arithmetic operations of sinusoidal functions are not convenient as they will involve using trigonometric identities. However, we can consider the phasor The sum of the two sinusoidal function can now be found as the real part of the rotating vector sum: The addition can be more easily carried out in the phasor form as vectors in the complex plane, than in the time domain. Specifically, consider two sinusoidal functions where and are two vectors in the complex plane with different magnitudes and initial phases called phasors When multiplied by , these vectors start rotating CCW in the complex plane. , and represent the functions in terms of their phasors representing their amplitudes and phases only. and then taking the real part: or Example
Why does current lead the voltage in capacitor? Best way is to consider an uncharged cap. A switch is closed & current enters the cap. The current is full value, a constant current source or a constant voltage source plus a resistor. At time t = 0+, the current i is maximum value, if the voltage source value is V, & resistance is R, then i(t=0+) = V/R. But the cap starts uncharged, Q=0, & V=0. As the voltage increases, the current decreases, eventually the cap reaches the source voltage & current tends to zero. Another thought is that current in a cap can change quickly/abruptly but voltage in a cap changes gradually/slowly. But changing cap voltage is changing its energy, needing work to be done. In the ac domain. i = C*dv/dt. Did I help? Claude
Angular frequency Angular frequency ω (in radians per second), is larger than frequency ν (in cycles per second, also called Hz), by a factor of 2π. This figure uses the symbol ν, rather than f to denote frequency. In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. is sometimes used as a synonym for the vector quantity angular velocity.[1] where: ω is the angular frequency or angular speed (measured in radians per second), T is the period (measured in seconds), Units[edit] In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. Examples[edit] A sphere rotating around an axis. Circular motion[edit] Oscillations of a spring[edit] An object attached to a spring will oscillate. where LC circuits[edit]
Calculator Tab • Free Online Scientific Calculator table of contents calculator Quick start Calculator Tab is a free online scientific calculator which works like your regular calculator. One feature that sets it appart from other calculators is that it's memory bank can store an unlimited amount of numbers and descriptions of these numbers for an indefinite length of time. The stored numbers can be sorted by date, by the number of uses or by name. This calculator follows the standard order of operations. . button. Calculator Tab will not allow you to make ambiguous enteries and will tell you, what is not allowed if you try to make such an entry. the entry of will generate an error telling you, that you first need to enter a number before continuing with the calculation. will be ignored and you can continue with your calculation as though you had not entered it. Features Using the memory function There are two possibilities to store a value in the memory bank:1. button you can quickly store the displayed value in the memory bank. .2. and .