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यथादृश्यविकिटेक्स्ट

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12:44, 23 फ़रवरी 2011 का अवतरण

यह लेख एक आधार है। जानकारी जोड़कर इसे बढ़ाने में विकिपीडिया की मदद करें।

प्रेरकत्व (inductor or a reactor) एक वैद्युत अवयव है जिसमें कोई विद्युत धारा प्रवाहित करने पर यह चुम्बकीय क्षेत्र के रूप में उर्जा का भंडारण करता है। प्रेरकत्व द्वारा चुम्बकीय उर्जा के भंडारण की क्षमता को इसका प्रेरकत्व (inductance) कहा जाता है और इसे मापने की इकाई हेनरी है।

उपयोग

वैद्युत फिल्टर बनाने के लिये
उर्जा भंडारित करने के लिये ( E = L.I²/2 )
इम्पीडैंस मैचिंग के लिये
ट्यूबलाइट आदि को जलाने के लिये आरम्भ में हजारों वोल्ट पैदा करने एवं जलने के बाद उससे बहने वाली धारा को सीमित रखने के लिये।
पुरानी कारों एवं स्कूटरों आदि में स्पार्क पैदा करने के लिये (इग्नीशन क्वायल)

प्रेरकत्व गणना के लिये सूत्र

संरचना	सूत्र	प्रतीकों के अर्थ	टिप्पणी
Cylindrical air-core coil^[1]	$L={\frac {\mu _{0}KN^{2}A}{l}}$	L = inductance in henries (H) μ₀ = permeability of free space = 4 $\pi$ × 10⁻⁷ H/m K = Nagaoka coefficient^[1] N = number of turns A = area of cross-section of the coil in square metres (m²) l = length of coil in metres (m)
Straight wire conductor ^[2]	$L={\frac {\mu _{0}}{2\pi }}\left[l\ln {\frac {l+{\sqrt {l^{2}+c^{2}}}}{c}}-{\sqrt {l^{2}+c^{2}}}+c\right]$ $+{\frac {\mu }{2\pi }}o\left({\frac {l}{4+c{\sqrt {\frac {2\omega \mu }{\rho }}}}}\right)$	L = inductance l = cylinder length c = cylinder radius μ₀ = vacuum permeability = $4\pi$ nH/cm μ = conductor permeability p = resistivity ω = phase rate	exact if ω = 0 or ω = ∞
	$L=0.2l\left(\ln {\frac {4l}{d}}-1\right)$ -0+3%	L = inductance (µH) l = length of conductor (mm) d = diameter of conductor (mm) f = frequency	Cu or Al l > 100 d d² f > 1 mm² MHz
	$L=0.2l\left(\ln {\frac {4l}{d}}-{\frac {3}{4}}\right)$ +0-3%	L = inductance (µH) l = length of conductor (mm) d = diameter of conductor (mm) f = frequency	Cu or Al l > 100 d d² f < 1 mm² MHz
Short air-core cylindrical coil^[3]	$L={\frac {r^{2}N^{2}}{9r+10l}}$	L = inductance (µH) r = outer radius of coil (in) l = length of coil (in) N = number of turns
Multilayer air-core coil^{[उद्धरण चाहिए]}	$L={\frac {0.8r^{2}N^{2}}{6r+9l+10d}}$	L = inductance (µH) r = mean radius of coil (in) l = physical length of coil winding (in) N = number of turns d = depth of coil (outer radius minus inner radius) (in)
Flat spiral air-core coil^{[उद्धरण चाहिए]}	$L={\frac {r^{2}N^{2}}{(20r+28d)}}$	L = inductance (µH) r = mean radius of coil (cm) N = number of turns d = depth of coil (outer radius minus inner radius) (cm)
Flat spiral air-core coil^{[उद्धरण चाहिए]}	$L={\frac {r^{2}N^{2}}{8r+11d}}$	L = inductance (µH) r = mean radius of coil (in) N = number of turns d = depth of coil (outer radius minus inner radius) (in)
Toroidal core (circular cross-section)^{[उद्धरण चाहिए]}	$L=\mu _{0}\mu _{r}{\frac {r^{2}N^{2}}{D}}$	L = inductance (H) μ₀ = permeability of free space = 4 $\pi$ × 10⁻⁷ H/m μ_r = relative permeability of core material r = radius of coil winding (m) N = number of turns D = overall diameter of toroid (m)

बाहरी कड़ियाँ

How stuff works The initial concept, made very simple
Capacitance and Inductance - A chapter from an online textbook
Spiral inductor models. Article on inductor characteristics and modeling.
Online coil inductance calculator. Online calculator calculates the inductance of conventional and toroidal coils using formulas 3, 4, 5, and 6, above.
AC circuits
Understanding coils and transforms

↑ ^अ ^आ Nagaoka, Hantaro (1909-05-06). "The Inductance Coefficients of Solenoids [1]". 27. Journal of the College of Science, Imperial University, Tokyo, Japan: 18. Cite journal requires |journal= (मदद); |title= में बाहरी कड़ी (मदद)
↑ The Self and Mutual Inductances of Linear Conductors, By Edward B. Rosa, Bulletin of the Bureau of Standards, Vol.4, No.2, 1908, p301-344
↑ ARRL Handbook, 66th Ed. American Radio Relay League (1989).

[Nagaoka-1] अ ^आ Nagaoka, Hantaro (1909-05-06). "The Inductance Coefficients of Solenoids [1]". 27. Journal of the College of Science, Imperial University, Tokyo, Japan: 18. Cite journal requires |journal= (मदद); |title= में बाहरी कड़ी (मदद)

[2] The Self and Mutual Inductances of Linear Conductors, By Edward B. Rosa, Bulletin of the Bureau of Standards, Vol.4, No.2, 1908, p301-344

[3] ARRL Handbook, 66th Ed. American Radio Relay League (1989).

[1]

[2]

[3]

@@ पंक्ति 10: / पंक्ति 10: @@
 * ट्यूबलाइट आदि को जलाने के लिये आरम्भ में हजारों वोल्ट पैदा करने एवं जलने के बाद उससे बहने वाली धारा को सीमित रखने के लिये।
 * पुरानी कारों एवं स्कूटरों आदि में स्पार्क पैदा करने के लिये (इग्नीशन क्वायल)
+==प्रेरकत्व गणना के लिये सूत्र==
+{| class="wikitable"
+ ! संरचना
+ ! सूत्र
+ ! प्रतीकों के अर्थ
+ | टिप्पणी
+ |-
+ ! Cylindrical air-core coil<ref name=Nagaoka>{{cite journal|last=Nagaoka|first=Hantaro|authorlink=Hantaro Nagaoka|title=The Inductance Coefficients of Solenoids [http://www.g3ynh.info/zdocs/refs/Nagaoka1909/index.html#31]|publisher=Journal of the College of Science, Imperial University, Tokyo, Japan|page=18|volume=27|date=1909-05-06}}</ref>
+ | <math>L=\frac{\mu_0KN^2A}{l}</math>
+ |
+*''L'' = inductance in [[Henry (unit)|henries]] (H)
+*''μ<sub>0</sub>'' = [[permeability of free space]] = 4''<math>\pi</math>'' × 10<sup>−7</sup> H/m
+*''K'' = Nagaoka coefficient<ref name=Nagaoka/>
+*''N'' = number of turns
+*''A'' = area of cross-section of the coil in [[square metre]]s (m<sup>2</sup>)
+*''l'' = length of coil in metres (m)
+ |
+ |-
+ ! rowspan="3"|Straight wire conductor <ref>[http://www.g3ynh.info/zdocs/refs/Rosa1908/index.html The Self and Mutual Inductances of Linear Conductors, By Edward B. Rosa, Bulletin of the Bureau of Standards, Vol.4, No.2, 1908, p301-344]</ref>
+ | <math>L = \frac{\mu_{0}}{2\pi}\left[l\ln\frac{l+\sqrt{l^{2}+c^{2}}}{c}-\sqrt{l^{2}+c^{2}} + c \right]</math>
+<br /> <math> + \frac{\mu}{2\pi} o\left(\frac{l}{4+c\sqrt{\frac{2\omega\mu}{\rho}}}\right)</math>
+ |
+*''L'' = inductance
+*''l'' = cylinder length
+*''c'' = cylinder radius
+*''μ''<sub>0</sub> = vacuum permeability = <math>4\pi</math> nH/cm
+*''μ'' = conductor permeability
+*''p'' = resistivity
+*''ω'' = phase rate
+ | exact if ω = 0 or ω = ∞
+ |-
+ | <math>L = 0.2 l\left(\ln\frac{4l}{d}-1\right)</math> -0+3%
+ |
+*''L'' = inductance (µH)
+*''l'' = length of conductor (mm)
+*''d'' = diameter of conductor (mm)
+*''f'' = frequency
+ |
+* Cu or Al
+* ''l'' > 100 ''d''
+* ''d''<sup>2</sup> ''f'' > 1 mm<sup>2</sup> MHz
+ |-
+ | <math>L = 0.2 l\left(\ln\frac{4l}{d}-\frac{3}{4}\right)</math> +0-3%
+ |
+*''L'' = inductance (µH)
+*''l'' = length of conductor (mm)
+*''d'' = diameter of conductor (mm)
+*''f'' = frequency
+ |
+* Cu or Al
+* ''l'' > 100 ''d''
+* ''d''<sup>2</sup> ''f'' < 1 mm<sup>2</sup> MHz
+ |-
+ ! Short air-core cylindrical coil<ref>ARRL Handbook, 66th Ed. American Radio Relay League (1989).</ref>
+ | <math>L=\frac{r^2N^2}{9r+10l}</math>
+ |
+*''L'' = inductance (µH)
+*''r'' = outer radius of coil (in)
+*''l'' = length of coil (in)
+*''N'' = number of turns
+ |-
+ ! Multilayer air-core coil{{Citation needed|date=November 2010}}
+ | <math>L = \frac{0.8r^2N^2}{6r+9l+10d}</math>
+ |
+*''L'' = inductance (µH)
+*''r'' = mean radius of coil (in)
+*''l'' = physical length of coil winding (in)
+*''N'' = number of turns
+*''d'' = depth of coil (outer radius minus inner radius) (in)
+ |-
+ ! rowspan="2"|Flat spiral air-core coil{{Citation needed|date=November 2010}}
+ | <math>L=\frac{r^2N^2}{(20r+28d)}</math>
+ |
+*''L'' = inductance (µH)
+*''r'' = mean radius of coil (cm)
+*''N'' = number of turns
+*''d'' = depth of coil (outer radius minus inner radius) (cm)
+ |-
+ | <math>L=\frac{r^2N^2}{8r+11d}</math>
+ |
+*''L'' = inductance (µH)
+*''r'' = mean radius of coil (in)
+*''N'' = number of turns
+*''d'' = depth of coil (outer radius minus inner radius) (in)
+ |-
+ ! Toroidal core (circular cross-section){{Citation needed|date=November 2010}}
+ | <math>L=\mu_0\mu_r\frac{r^2N^2}{D}</math>
+ |
+*''L'' = inductance (H)
+*''μ<sub>0</sub>'' = [[Permeability (electromagnetism)|permeability]] of [[vacuum|free space]] = 4''<math>\pi</math>'' × 10<sup>−7</sup> H/m
+*''μ<sub>r</sub>'' = relative permeability of core material
+*''r'' = radius of coil winding (m)
+*''N'' = number of turns
+*''D'' = overall diameter of toroid (m)
+ |}
 ==बाहरी कड़ियाँ==