{"id":152615,"date":"2022-03-23T10:00:26","date_gmt":"2022-03-23T04:30:26","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=152615"},"modified":"2025-06-20T17:12:49","modified_gmt":"2025-06-20T11:42:49","slug":"blog-iit-jee-dimensions-of-potential-difference","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/","title":{"rendered":"Dimensions of Potential Difference"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#What_is_Potential_Difference\" title=\"What is Potential Difference?\">What is Potential Difference?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#Unit_of_Potential_Difference\" title=\"Unit of Potential Difference\">Unit of Potential Difference<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#Potential_difference_as_a_scalar_quantity\" title=\"Potential difference as a scalar quantity\">Potential difference as a scalar quantity<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#Dimensional_Formula_of_Potential_Difference\" title=\"Dimensional Formula of Potential Difference\">Dimensional Formula of Potential Difference<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#Potential_Difference_and_EMF_of_a_Cell\" title=\"Potential Difference and EMF of a Cell\">Potential Difference and EMF of a Cell<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#Half-cell_reactions\" title=\"Half-cell reactions\">Half-cell reactions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#Difference_between_Cell_Potential_and_EMF\" title=\"Difference between Cell Potential and EMF\">Difference between Cell Potential and EMF<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/dimensions-of-potential-difference\/#FAQs_on_Dimensions_of_Potential_Difference\" title=\"FAQs on Dimensions of Potential Difference\">FAQs on Dimensions of Potential Difference<\/a><\/li><\/ul><\/nav><\/div>\n<p>Potential difference plays a crucial role in the flow of <strong>electric current<\/strong>. The definition of electric potential states that the amount of work required to move a positive unit charge from infinity to a point is the potential of that point. When there is a difference between the potential of two points, a potential gradient is formed, which allows current to flow.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Potential_Difference\"><\/span>What is Potential Difference?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Potential difference refers to the amount of work required to move a unit charge from one point to another. One point will have a higher potential, while the other will have a lower potential. Work must be done when moving a positive charge from a point of lower potential to a point of higher potential.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Unit_of_Potential_Difference\"><\/span>Unit of Potential Difference<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The <strong>unit of potential difference<\/strong> is the <strong>volt (V)<\/strong>. One volt is defined as the potential difference between two points in a circuit when one joule of energy is used to move one coulomb of charge between those two points.<\/p>\n<p>Mathematically, it is expressed as:<\/p>\n<p><strong>1 V = 1 Joule \/ 1 Coulomb<\/strong><\/p>\n<p>This relationship illustrates that a potential difference of 1 volt exists when 1 joule of work is done to move 1 coulomb of charge between two points in an electric field.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/blog\/employability-skills-for-class-10\/\">Employability Skills for Class 10 Students<\/a><\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Potential_difference_as_a_scalar_quantity\"><\/span>Potential difference as a scalar quantity<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Potential difference is considered a scalar quantity because it only has magnitude and no directional property. Unlike vector quantities, which require both magnitude and direction (like force or velocity), potential difference is concerned solely with the difference in electric potential energy between two points, and it does not involve any inherent directionality.<\/p>\n<p>In an electric circuit, potential difference tells us how much energy per charge is being used or provided, but it doesn&#8217;t need a directional component to describe this; it simply measures the difference in energy levels (in volts) across two points. Therefore, it can be added or subtracted directly without considering direction, making it scalar by nature.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dimensional_Formula_of_Potential_Difference\"><\/span>Dimensional Formula of Potential Difference<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>From the definition discussed above, the potential difference can be written as :<\/p>\n<p><strong>\u0394V= \u0394 W\/Q<\/strong><\/p>\n<p>Q = electric charge<\/p>\n<p>W = work done<\/p>\n<p>So, dimension of potential difference= dimension of work done \/ dimension of electric charge.<\/p>\n<p>W= F.S<\/p>\n<p>So, dimension of W = [MLT<sub>-2<\/sub>] x [L] = [ML<sub>2<\/sub>T<sub>-2<\/sub>]\n<p>So, dimension of \u0394V = [ML<sub>2<\/sub>T<sub>-2<\/sub>] \/  [IT] = [MI<sub>-1<\/sub>L<sub>2<\/sub>T<sub>-3<\/sub>]\n<p>So, the dimension of potential difference is [MI-1L2T-3]\n<h3><span class=\"ez-toc-section\" id=\"Potential_Difference_and_EMF_of_a_Cell\"><\/span>Potential Difference and EMF of a Cell<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The potential difference between the electrodes of a <strong>Galvanic cell<\/strong> is called the <strong>cell potential<\/strong>. It is defined as the difference between the <strong>reduction potentials<\/strong> of the anode and cathode, measured in volts.<\/p>\n<p>When no current is drawn from the cell, the potential difference is termed the <strong>EMF (electromotive force)<\/strong>. The EMF is positive and is calculated as the difference between the potentials of the half-cell on the right and the half-cell on the left.<\/p>\n<p><strong>EMF Formula:<\/strong><\/p>\n<p>Ecell = Eright \u2013 Eleft \u2026.. (eq1)<\/p>\n<p><strong>Cell Reaction:<\/strong><\/p>\n<p>In this example, the copper electrode acts as the anode, and the silver electrode is the cathode. The overall reaction is:<\/p>\n<p>Cu (s) + 2Ag+ (aq) \u2192 Cu2+ (aq) + 2 Ag (s) \u2026\u2026. (eq2)<\/p>\n<p>Here, (s) indicates the solid state of the electrode, and (aq) represents the ions dissolved in water.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Half-cell_reactions\"><\/span>Half-cell reactions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Cathode (reduction): 2Ag<sup>+<\/sup>(aq)+2e<sup>\u2212<\/sup>\u21922Ag(s)<\/li>\n<li>Anode (oxidation): Cu(s)\u2192Cu<sup>2+<\/sup>(aq)+2e<sup>\u2212<\/sup><\/li>\n<\/ul>\n<p>The overall cell reaction is the summation of these two half-cell reactions.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Difference_between_Cell_Potential_and_EMF\"><\/span>Difference between Cell Potential and EMF<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<th><strong>Cell Potential<\/strong><\/th>\n<th><strong>EMF (Electromotive Force)<\/strong><\/th>\n<\/tr>\n<tr>\n<td>The potential difference between two electrodes when current is flowing through the cell.<\/td>\n<td>The maximum potential difference between two electrodes when no current is flowing (open circuit condition).<\/td>\n<\/tr>\n<tr>\n<td>Measured when the circuit is closed and the cell is in use.<\/td>\n<td>Measured when the circuit is open, and no current is flowing.<\/td>\n<\/tr>\n<tr>\n<td>Affected by current, internal resistance, and external load.<\/td>\n<td>Independent of current and load, remains constant.<\/td>\n<\/tr>\n<tr>\n<td>Usually lower than EMF due to internal resistance and energy losses.<\/td>\n<td>Represents the maximum theoretical voltage of the cell.<\/td>\n<\/tr>\n<tr>\n<td>Refers to the actual voltage output during operation.<\/td>\n<td>Refers to the theoretical maximum voltage under ideal conditions (no load).<\/td>\n<\/tr>\n<tr>\n<td>The voltage measured across a battery powering a device.<\/td>\n<td>The open-circuit voltage of a battery without any load attached.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Dimensions_of_Potential_Difference\"><\/span>FAQs on Dimensions of Potential Difference<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"&#8221;What\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"&#8221;The\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n.&#8221; image-0=&#8221;&#8221; headline-1=&#8221;h3&#8243; question-1=&#8221;What is the dimension of PE?&#8221; answer-1=&#8221;The dimensional formula of Potential Energy (PE) is [ML\u00b2T\u207b\u00b2], which corresponds to mass, length squared, and time inverse squared.&#8221; image-1=&#8221;&#8221; headline-2=&#8221;h3&#8243; question-2=&#8221;What is the dimensional formula of electric potential Class 12?&#8221; answer-2=&#8221;The dimensional formula of electric potential is [M\u00b9L\u00b2T\u207b\u00b3I\u207b\u00b9], where it is derived from energy per unit charge\u200b.&#8221; image-2=&#8221;&#8221; headline-3=&#8221;h3&#8243; question-3=&#8221;What is the dimensional formula of voltage difference?&#8221; answer-3=&#8221;The dimensional formula of voltage difference is also [M\u00b9L\u00b2T\u207b\u00b3I\u207b\u00b9], as voltage represents potential difference between two points.&#8221; image-3=&#8221;&#8221; headline-4=&#8221;h3&#8243; question-4=&#8221;What is the SI unit of potential difference and its dimensions?&#8221; answer-4=&#8221;The SI unit of potential difference is the volt (V), and its dimensional formula is [M\u00b9L\u00b2T\u207b\u00b3I\u207b\u00b9]&#8221; image-4=&#8221;&#8221; headline-5=&#8221;h3&#8243; question-5=&#8221;Are voltage and potential difference the same?&#8221; answer-5=&#8221;Yes, voltage and potential difference refer to the same concept: the difference in electric potential between two points.&#8221; image-5=&#8221;&#8221; count=&#8221;6&#8243; html=&#8221;true&#8221; css_class=&#8221;&#8221;]\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Potential difference plays a crucial role in the flow of electric current. The definition of electric potential states that the [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Potential Difference","_yoast_wpseo_title":"Dimensions of Potential Difference- Explained with Simple Examples | IL","_yoast_wpseo_metadesc":"Learn about the dimensions of potential difference, how it impacts electric charge flow, and its importance in physics. 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