{"id":710,"date":"2007-05-25T16:21:52","date_gmt":"2007-05-25T21:21:52","guid":{"rendered":"http:\/\/softbeam.net\/hobby\/?p=710"},"modified":"2007-05-25T16:21:52","modified_gmt":"2007-05-25T21:21:52","slug":"electrical-conductivity","status":"publish","type":"post","link":"https:\/\/softbeam.net\/hobby\/?p=710","title":{"rendered":"electrical conductivity"},"content":{"rendered":"<p><strong>Electrical conductivity<\/strong> or <strong>specific conductivity<\/strong> is a measure of a material&#8217;s ability to <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_conduction\" title=\"Electrical conduction\">conduct<\/a> an <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electric_current\" title=\"Electric current\">electric current<\/a>. When an <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_potential_difference\" title=\"Electrical potential difference\">electrical potential difference<\/a> is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity \u03c3 is defined as the ratio of the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Current_density\" title=\"Current density\">current density<\/a> <img decoding=\"async\" src=\"http:\/\/upload.wikimedia.org\/math\/4\/e\/d\/4ede6b55c75fdc76e3d957e44ae92b07.png\" class=\"tex\" alt=\"\\mathbf{J}\" \/> to the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electric_field\" title=\"Electric field\">electric field<\/a> strength <img decoding=\"async\" src=\"http:\/\/upload.wikimedia.org\/math\/5\/e\/b\/5eb237ccb8c2716d347ab313cad7918e.png\" class=\"tex\" alt=\"\\mathbf{E}\" \/>:<\/p>\n<dl>\n<dd><img decoding=\"async\" src=\"http:\/\/upload.wikimedia.org\/math\/2\/a\/1\/2a1ed92dee1588215bc2d77d0ed2697f.png\" class=\"tex\" alt=\"\\mathbf{J} = \\sigma \\mathbf{E}\" \/>.<\/dd>\n<\/dl>\n<p>It is also possible to have materials in which the conductivity is <a href=\"http:\/\/en.wikipedia.org\/wiki\/Anisotropic\" title=\"Anisotropic\">anisotropic<\/a>, in which case \u03c3 is a 3\u00d73 <a href=\"http:\/\/en.wikipedia.org\/wiki\/Matrix_%28mathematics%29\" title=\"Matrix (mathematics)\">matrix<\/a> (or more technically a rank-2 <a href=\"http:\/\/en.wikipedia.org\/wiki\/Tensor\" title=\"Tensor\">tensor<\/a>) which is generally <a href=\"http:\/\/en.wikipedia.org\/wiki\/Symmetric_matrix\" title=\"Symmetric matrix\">symmetric<\/a>.<\/p>\n<p>Conductivity is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Reciprocal_%28mathematics%29\" title=\"Reciprocal (mathematics)\">reciprocal<\/a> (<a href=\"http:\/\/en.wikipedia.org\/wiki\/Invertible_matrix\" title=\"Invertible matrix\">inverse<\/a>) of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_resistivity\" title=\"Electrical resistivity\">electrical resistivity<\/a> and has the SI units of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Siemens_%28unit%29\" title=\"Siemens (unit)\">siemens<\/a> per <a href=\"http:\/\/en.wikipedia.org\/wiki\/Metre\" title=\"Metre\">metre<\/a> (S\u00b7m<sup>-1<\/sup>) i.e. if the electrical conductance between opposite faces of a 1-metre cube of material is 1 siemens then the material&#8217;s electrical conductivity is 1 siemens per metre. Electrical conductivity is commonly represented by the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Greek_alphabet\" title=\"Greek alphabet\">Greek letter<\/a> <a href=\"http:\/\/en.wikipedia.org\/wiki\/Sigma_%28letter%29\" title=\"Sigma (letter)\">\u03c3<\/a>, but <a href=\"http:\/\/en.wikipedia.org\/wiki\/Kappa\" title=\"Kappa\">\u03ba<\/a> or <a href=\"http:\/\/en.wikipedia.org\/wiki\/Gamma\" title=\"Gamma\">\u03b3<\/a> are also occasionally used.<\/p>\n<p>Also:<\/p>\n<p>For a device with <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_resistance\" title=\"Electrical resistance\">electrical resistance<\/a> <em>R<\/em>, the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_conductance\" title=\"Electrical conductance\">conductance<\/a> <em>G<\/em> is defined as<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/upload.wikimedia.org\/math\/4\/7\/9\/47942fe03833725d83b1016c5dd7d8c5.png\" class=\"tex\" alt=\"G = \\frac1R = \\frac{I}V,\" \/><\/p>\n<p>where<\/p>\n<ul>\n<li><em>G<\/em> is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_conductance\" title=\"Electrical conductance\">conductance<\/a>,<\/li>\n<li><em>R<\/em> is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Electrical_resistance\" title=\"Electrical resistance\">resistance<\/a>,<\/li>\n<li><em>I<\/em> is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Current_%28electricity%29\" title=\"Current (electricity)\">current<\/a> through the device and<\/li>\n<li><em>V<\/em> is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Voltage\" title=\"Voltage\">voltage<\/a> (electrical potential difference) across the device.<\/li>\n<\/ul>\n<p>The unit <strong>siemens<\/strong> for the conductance <em>G<\/em> is defined by 1 S = 1 A\/V = 1 A<sup>2<\/sup>\/W = 1 kg<sup>\u22121<\/sup>\u00b7m<sup>\u22122<\/sup>\u00b7s<sup>3<\/sup>\u00b7A<sup>2<\/sup> =1 \u03a9<sup>-1<\/sup> = 1 kg<sup>\u22121<\/sup>\u00b7m<sup>\u22122<\/sup>\u00b7s<sup>1<\/sup>\u00b7C<sup>2<\/sup>. So for a device with conductance 1 S, then the current through it with a 1 V voltage across it is 1 A, and for each extra V of voltage across it the current through it increases by 1 A.<\/p>\n<p>Some tricks:<\/p>\n<p>conductivity (S m<sup>\u22121<\/sup>) = specific conductance (S)<\/p>\n<p>resistance (\u03a9 m<sup>\u22121<\/sup>) = specific resistance (\u03a9)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Electrical conductivity or specific conductivity is a measure of a material&#8217;s ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity \u03c3 is defined as the ratio of the current density to the electric field strength : &hellip; <a href=\"https:\/\/softbeam.net\/hobby\/?p=710\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;electrical conductivity&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-710","post","type-post","status-publish","format-standard","hentry","category-physical"],"_links":{"self":[{"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=\/wp\/v2\/posts\/710","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=710"}],"version-history":[{"count":0,"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=\/wp\/v2\/posts\/710\/revisions"}],"wp:attachment":[{"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=710"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=710"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/softbeam.net\/hobby\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}