Leading and lagging current
Leading and lagging current are phenomena that occur as a result of
In electric power flow, it is important to know how much current is leading or lagging because it creates the
Angle notation
In this equation, the value of theta is the important factor for leading and lagging current. As mentioned in the introduction above, leading or lagging current represents a time shift between the current and voltage sine curves, which is represented by the angle by which the curve is ahead or behind of where it would be initially. For example, if θ is zero, the curve will have amplitude zero at time zero.
Lagging current
Lagging current can be formally defined with respect to “an alternating current that reaches its maximum value up to 90 degrees later than the voltage that produces it.” This means that current lags the voltage when , the angle of the current sine wave with respect to an arbitrarily chosen reference, is less than , the angle of the voltage sine wave with respect to the same reference. Therefore, current can quickly be identified as lagging if the angle is positive. For example, if the voltage angle is zero, current will be lagging if is negative. This is often the case because voltage is taken as the reference.
In circuits with primarily inductive loads, current lags the voltage. This happens because in an inductive load, it is the induced electromotive force that causes the current to flow. Note that in the definition above, the current is produced by the voltage. The induced electromotive force is caused by a change in the magnetic flux linking the coils of an inductor.
Leading current
Leading current can be formally defined as “an alternating current that reaches its maximum value up to 90 degrees ahead of the voltage that it produces.” This means that the current leads the voltage when , the angle of the current sine wave with respect to an arbitrarily chosen reference is greater than , the angle of the voltage sine wave with respect to the same reference. Therefore, current can quickly be identified as leading if the angle is negative. For example, if the voltage angle is zero, current will be leading if is positive. This is often the case because voltage is taken as the reference.
In circuits with primarily capacitive loads, current leads the voltage. This is true because current must first flow to the two plates of the capacitor, where charge is stored. Only after charge accumulates at the plates of a capacitor is a voltage difference established. The behavior of the voltage is thus dependent on the behavior current and on how much charge accumulates. This is why the formal definition states that the current produces the voltage.In other words when A.C voltage start increasing charge start to accumulate across capacitor plates i.e current start to flow.This increasing charge develope potential difference across capacitor that reduces current.On the other hand when A.C voltage is decreasing higher voltage of charged capacitor causes current to flow in opposite direction and capacitor is discharged and vice versa.
Visualizing leading and lagging current
A simple
Historical documents concerning leading and lagging currents
An early source of data is an article from the 1911 American Academy of Arts and Sciences by Arthur E. Kennelly. Kennelly uses conventional methods in solving vector diagrams for oscillating circuits, which can also include alternating current circuits as well.
See also
- Electrical impedance
- Power factor
- Volt-ampere
- Volt-ampere reactive
Notes
References:
- ^ Nilsson p. 338
- ^ Wiley-Interscience. pp. 49–66.
References
- Bowick, Chris, John Blyler, and Cheryl J. Ajluni. RF Circuit Design. 2nd ed. Amsterdam: Newnes/Elsevier, 2008. Print.
- Gaydecki, Patrick. Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design. 2nd ed. London: Institution of Electrical Engineers, 2004. Print
- Gilmore, Rowan, and Les Besser. Passive Circuits and Systems. Boston [u.a.: Artech House, 2003. Print.
- Hayt, W. H., and J. E. Kemmerly. Engineering Circuit Analysis. 2nd ed. New York: McGraw-Hill, 1971. Print.
- Kennelly, Arthur E. "Vector-Diagrams of Oscillating-Current Circuits." American Academy of Arts & Sciences 46.17 (1911): 373–421. Jstor. ITHAKA. Web. 1 May 2012. <https://www.jstor.org/stable/20022665>.
- "Lagging Current." TheFreeDictionary.com. Web. 1 May 2012. (http://encyclopedia2.thefreedictionary.com/lagging_current)
- "Leading Current." TheFreeDictionary.com. Web. 1 May 2012. (http://encyclopedia2.thefreedictionary.com/leading_current)
- Nilsson, James William; Riedel, Susan A. (2008). Electric circuits (8th ed.). Prentice Hall. p. 338. ISBN 0-13-198925-1, Chapter 9, page 338
- Smith, Ralph J. Circuit Devices and Systems. 3rd ed. New York: John Wiley & Sons, 1976. Print.
- Glover, Duncan J. Power System Analysis and Design. 5th ed. Cengage Learning, 2014.
- Masters, G. Renewable and Efficient Electric Power Systems. 2nd ed. Wiley, 2004.