where did the energy come from?<\/p>\n
A parallel-plate capacitor is charged and then kept connected with a 5V battery.<\/p>\n
Then, the plate separation is decreased by a factor of 4, d_new=1\/4 d_old,<\/p>\n
please type in a number into the box to determine how everything changes.<\/p>\n
(If something doesn’t change, please type in 1 to answer X_new= 1 X_old.)<\/p>\n
(a) By what fraction does the capacitance change? C_new= C_old;<\/p>\n
(b) By what fraction does the amount of charge change? Q_new= Q_old (When the battery is connected, charges can keep moving and the charge may not stay to be the same.)<\/p>\n
(c) By what fraction does the voltage difference between the two plates change? ?V_new= ?V_old (When the battery is always connected, the voltage difference across the capacitor will be always equal to the battery voltage).<\/p>\n
(d) By what fraction does the energy stored in the capacitor change? U_new= U_old<\/p>\n
Does it make sense? Let’s check, considering the amount of charge and the area of the plate,<\/p>\n
(e) by what fraction does the amount of charge density change? ?_new= ?_old<\/p>\n
(f) Consider how E is related to the charge density, by what fraction does the E field change? E_new= E_old.<\/p>\n
Considering how E, d and voltage difference are related, does it make sense now, how E, and d change to keep the voltage difference unchanged?<\/p>\n
Please explain why the energy stored in the capacitor changes? If it increased, where did the energy come from? If it decreased, where could the energy go?<\/p>\n","protected":false},"excerpt":{"rendered":"
where did the energy come from? A parallel-plate capacitor is charged and then kept connected with a 5V battery. Then, the plate separation is decreased by a factor of 4, d_new=1\/4 d_old, please type in a number into the box Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-239387","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/239387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=239387"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/239387\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=239387"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=239387"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=239387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}