resistance           package:ResistorArray           R Documentation

_R_e_s_i_s_t_a_n_c_e _f_o_r _a_r_b_i_t_r_a_r_i_l_y _c_o_n_n_e_c_t_e_d _n_e_t_w_o_r_k_s _o_f _r_e_s_i_s_t_o_r_s

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

     Given a resistance matrix, return the resistance between two
     specified nodes.

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

     resistance(A, earth.node, input.node, current.input.vector=NULL, give.pots = FALSE)

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

       A: Resistance matrix

earth.node: Number of node that is earthed

input.node: Number of node at which *current* is put in: a nominal 1
          Amp

current.input.vector: Vector of currents that are fed into each node. 
          If supplied, overrides the value of 'input.node', and
          effectively sets 'give.pots' to 'TRUE' because if various
          currents are fed into the network at various points, the
          concept of "resistance" becomes meaningless.

          Setting this argument to 'c(0,...,0,1,0,..0)' (where the "1"
          is element 'jj') is equivalent to not setting
          'current.input.vector' and setting 'input.node' to 'jj'.  

give.pots: Boolean, with 'TRUE' meaning to return the potential of each
          node ('out.node' being at zero potential); and default
          'FALSE' meaning to return just the resistance between
          'in.node' and 'out.node'.

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

     The function's connection to resistor physics is quite opaque. It
     is effectively a matrix version of Kirchoff's law, that the
     (algebraic) sum of currents into a node is zero.

_N_o_t_e:

     This function is essentially a newbie wrapper for 'circuit()',
     which solves a much more general problem.  The function documented
     here, however, is clearer and (possibly) faster; it also gives an
     explicit resistance if 'give.pots' is not set.

     Use function 'currents()' (or 'currents.matrix()') to calculate
     the currents flowing in the resistor array.

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

     Robin K. S. Hankin

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

     B. Bollob\'{a}s, 1998.  "Modern Graph Theory".  Springer.

     F. Y. Wu, 2004.  "Theory of resistor networks: the two point
     resistance", Journal of Physics A, volume 37, pp6653-6673

     G. Venezian 1994. "On the resistance between two points on a
     grid", American Journal of Physics, volume 62, number 11,
     pp1000-1004.

     J. Cserti 2000.  "Application of the lattice Green's function for
     calculating the resistance of an infinte network of resistors",
     American Journal of Physics, volume 68, number 10, p896-906

     D. Atkinson and F. J. van Steenwijk 1999.  "Infinite resistive
     lattices", American Journal of Physics, volume 67, number 6,
     pp486-492

_S_e_e _A_l_s_o:

     'array.resistance'

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

       resistance(cube(),earth.node=1, input.node=7) #known to be 5/6 ohm
       resistance(cube(),1,7, give=TRUE)

