cube              package:ResistorArray              R Documentation

_S_p_e_c_i_m_e_n _c_o_n_d_u_c_t_a_n_c_e _m_a_t_r_i_c_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     Various conductance matrices for simple resistor configurations
     including a skeleton cube

_U_s_a_g_e:

     cube(x=1)
     octahedron(x=1)
     tetrahedron(x=1)
     dodecahedron(x=1)
     icosahedron(x=1)

_A_r_g_u_m_e_n_t_s:

       x: Reistance of each edge.  See details section

_D_e_t_a_i_l_s:

     Function 'cube()' returns an eight-by-eight conductance matrix for
     a skeleton cube of 12 resistors.  Each row/column corresponds to
     one of the 8 vertices that are the electrical nodes of the
     compound resistor.

     In one orientation, node 1 has position 000, node 2 position 001,
     node 3 position 101, node 4 position 100, node 5 position 010,
     node 6 position 011, node 7 position 111, and node 8 position 110.

     In 'cube()', 'x' is a vector of twelve elements (a scalar argument
     is interpreted as the resistance of each resistor) representing
     the twelve resistances of a skeleton cube.  In the orientation
     described below, the elements of 'x' correspond to R_12, R_14,
     R_15, R_23, R_26, R_34, R_37, R_48, R_56, R_58, R_67, R_78 (here
     R_ij is the resistancd between node i  and j).  This series is
     obtainable by reading the rows given by 'platonic("cube")'.  The
     pattern is general: edges are ordered first by the row number i,
     then column number j.

     In 'octahedron()', 'x' is a vector of twelve elements (again
     scalar argument is interpreted as the resistance of each resistor)
     representing the twelve resistances of a skeleton octahedron.  If
     node 1 is "top" and node 6 is "bottom", the elements of 'x'
     correspond to R_12, R_13, R_14, R_15, R_23, R_25, R_26, R_34,
     R_36,  R_45, R_46, R_56. This may be read off from the rows of
     'platonic("octahedron")'.

     To do a Wheatstone bridge, use 'tetrahedron()' with one of the
     resistances 'Inf'.  As a worked example, let us determine the
     resistance of a Wheatstone bridge with four resistances one ohm
     and one of two ohms; the two-ohm resistor is one of the ones
     touching the earthed node.

     To do this, first draw a tetrahedron with four nodes.  Then say we
     want the resistance between node 1 and node 3; thus edge 1-3 is
     the infinite one.   'platonic("tetrahedron")' gives us the order
     of the edges: 12, 13, 14, 23, 24, 34.  Thus the conductance matrix
     is given by 'jj <- tetrahedron(c(2,Inf,1,1,1,1))' and the
     resistance is given by 'resistance(jj,1,3)' [compare the
     analytical answer of 117/99 ohms].

_A_u_t_h_o_r(_s):

     Robin K. S. Hankin

_R_e_f_e_r_e_n_c_e_s:

     F. J. van Steenwijk "Equivalent resistors of polyhedral resistive
     structures", American Journal of Physics, 66(1), January 1988.

_E_x_a_m_p_l_e_s:

      resistance(cube(),1,7)  #known to be 5/6 ohm
      resistance(cube(),1,2)  #known to be 7/12 ohm

      resistance(octahedron(),1,6) #known to be 1/2 ohm
      resistance(octahedron(),1,5) #known to be 5/12 ohm

      resistance(dodecahedron(),1,5) 

