FFP12 2011 Udine 21-23 November 2011 CAPACITORS, TANKS, SPRINGS AND THE LIKE: A MULTIMEDIA TUTORIAL Assunta Bonanno, Michele Camarca, Peppino Sapia, P.E.R. Group, Physics Department – University of Calabria – 87036 Rende (CS) - Italy Abstract In this work we present an interactive multimedia tutorial allowing to comparatively explore the dynamical behavior of the “Two-capacitor system” and of others systems, quite different, but showing a very similar energetic behavior: i) two communicating tanks; ii) two coupled lossy springs “sharing elongation”; iii) plastic collision between two material points; iv) two coaxial, rotationally coupled, disks spinning around an axis. The aim of the work is to give learners useful insights on the fundamental subject of energy transformation. The tutorial, appropriate for high school and first year university students, is implemented in a form that makes it also suitable for classroom use with an Interactive White Board. 1. Introduction There is a well-known textbook problem (Halliday et Al., 1997; Lorrain et al., 1988) that every once in a while, since forty years, appears in the literature (Cuvaj, 1968; Powell, 1979; Sciamanda, 1996; Mita and Boufaida, 1999; Al-Jaber and Salih, 2000; Boykin et al., 2002): the so called “Two Capacitor Problem”, also present in on-line forums as “The Capacitor Conundrum” (Sciamanda, 1996). The problem concerns two capacitors, one of which ( 1 C ) charged, the other ( 2 C ) uncharged, which are connected at time t=0. Simple calculations show that in the process a fraction ( 29 2 1 2 C C C + of the initial electrostatic energy disappears, apparently giving rise to a paradox. The behavior of this system asks some questions usually worrying learners (first of all: where does lost electrostatic energy go?). The search for answering these questions allows, from a didactical point of view, to highlight many subtleties about energy transformation processes. In this regard, it is very useful comparing the two capacitors system with others systems, quite different, but showing a very similar energetic behavior: i) two communicating tanks containing a fluid, initially located in one of the two; ii) two coupled lossy springs “sharing elongation”; iii) plastic collision between two material points; iv) two coaxial, rotationally coupled, disks spinning around an axis. In this connection we present here an interactive multimedia tutorial allowing to comparatively explore the dynamical behavior of described systems. The tutorial (implemented in a form that makes it also suitable for classroom use with an Interactive White Board) is appropriate for high school and first year university students and has manifold goals; among others: i) to give learners useful insights on the fundamental subject of energy transformation; ii) to shed light on the role of dissipative phenomena in the achievement of equilibrium; iii) to illustrate the role of analogies in the study of physical phenomena, in the aim to allow students to get used to a proper identification of similarities between apparently different scientific subjects; iv) to pave the way for further quantitative treatment of the problem. In the present paper, after summarizing in section 2 the two-capacitor-problem family, we will describe, in section 3, the tutorial. In section 4, eventually, we draw some interesting conclusion. Figure 1: The two capacitor problem. A capacitor is initially charged, the other uncharged (left). Then capacitors are connected so to share the electric charge (right). In this process half the electrostatic energy “disappears”.