- 1 (206.85 KiB) Viewed 15 times
9 1 a р Z e 9 Somebody has built a cube-shaped object by using 12 identical resistors. In the figure above, each edge of the cube is a resistor with resiatance R. The cube is connected to a battery from the corners a and z so that a current I passes over the whole cube. The problem is to find the equivalent resistance Reg of the cube. If there were no symmetry, this problem would be extremely difficult. However, by using the symmetry, it is possible to find a quick solution. Convince yourself that the symmetry implies the following: • Currents in branches ae, af and ag are equal to each other. Currents in branches fr, fq, gr, gp, ep and eq are all equal to each other. Currents in branches pz, qz and rz are all equal to each other. - Using these, answer the following questions. (a) Write down the currents on the following branches along the indicated directions. On branch af flowing from a to f On branch fr flowing from f tor On branch rz flowing from r to za (b) Find the potential difference between a and z (in terms of R and I). Vaz (c) Finally, write down the equivalent resistance between points a and z (in terms of R). Reg Check