{"id":99,"date":"2022-07-14T00:09:37","date_gmt":"2022-07-14T00:09:37","guid":{"rendered":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/chapter\/solution-exercise-5\/"},"modified":"2022-07-21T16:33:04","modified_gmt":"2022-07-21T16:33:04","slug":"solution-exercise-5","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/chapter\/solution-exercise-5\/","title":{"raw":"Solution Exercise 5","rendered":"Solution Exercise 5"},"content":{"raw":"
\r\n

Calculate the apparent resistivity in the following arbitrary electrode configuration when a 5\u00a0mA current is injected between electrodes A<\/em> and B<\/em>, and 80\u00a0mV is measured between M<\/em> and N<\/em>.<\/p>\r\n

[latex]\\displaystyle K_{g}=\\frac{2\\pi }{\\frac{1}{\\overline{AM}}-\\frac{1}{\\overline{AN}}-\\frac{1}{\\overline{BM}}+\\frac{1}{\\overline{BN}}}[\/latex]<\/p>\r\n

[latex]\\displaystyle =\\frac{2\\pi }{\\frac{1}{2\\mathrm{m}}-\\frac{1}{3\\mathrm{m}}-\\frac{1}{4\\mathrm{m}}+\\frac{1}{3\\mathrm{m}}}[\/latex]<\/p>\r\n

[latex]\\displaystyle =25.1\\mathrm{m}[\/latex]<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\u03c1<\/em>a<\/em><\/sub><\/td>\r\n=<\/td>\r\nKg<\/em><\/sub><\/em>(\u0394V<\/em>\/I<\/em>)<\/td>\r\n<\/tr>\r\n
<\/td>\r\n=<\/td>\r\n25.1 m * 80 mV \/ 5 mA<\/td>\r\n<\/tr>\r\n
<\/td>\r\n=<\/td>\r\n400 ohm-m<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Return to Exercise 5<\/a><\/p>\r\n\r\n<\/div>","rendered":"

\n

Calculate the apparent resistivity in the following arbitrary electrode configuration when a 5\u00a0mA current is injected between electrodes A<\/em> and B<\/em>, and 80\u00a0mV is measured between M<\/em> and N<\/em>.<\/p>\n

[latex]\\displaystyle K_{g}=\\frac{2\\pi }{\\frac{1}{\\overline{AM}}-\\frac{1}{\\overline{AN}}-\\frac{1}{\\overline{BM}}+\\frac{1}{\\overline{BN}}}[\/latex]<\/p>\n

[latex]\\displaystyle =\\frac{2\\pi }{\\frac{1}{2\\mathrm{m}}-\\frac{1}{3\\mathrm{m}}-\\frac{1}{4\\mathrm{m}}+\\frac{1}{3\\mathrm{m}}}[\/latex]<\/p>\n

[latex]\\displaystyle =25.1\\mathrm{m}[\/latex]<\/p>\n\n\n\n\n\n
\u03c1<\/em>a<\/em><\/sub><\/td>\n=<\/td>\nKg<\/em><\/sub><\/em>(\u0394V<\/em>\/I<\/em>)<\/td>\n<\/tr>\n
<\/td>\n=<\/td>\n25.1 m * 80 mV \/ 5 mA<\/td>\n<\/tr>\n
<\/td>\n=<\/td>\n400 ohm-m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Return to Exercise 5<\/a><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":42,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-99","chapter","type-chapter","status-publish","hentry"],"part":158,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/99","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":4,"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/99\/revisions"}],"predecessor-version":[{"id":382,"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/99\/revisions\/382"}],"part":[{"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/parts\/158"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/99\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/wp\/v2\/media?parent=99"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/pressbooks\/v2\/chapter-type?post=99"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/wp\/v2\/contributor?post=99"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/electrical-imaging-for-hydrogeology\/wp-json\/wp\/v2\/license?post=99"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}