Results 1 to 2 of 2

Thread: double sum designation question..

  1. #1
    MHF Contributor
    Nov 2008

    double sum designation question..

    the telegan law basically states that the total sum of power is zero.
    my prof proved lik this:

    we choose a node (a point where more then one currents come together)

    and decide that the voltage on that node to be zero.
    we designate the voltages on the nodes to be $\displaystyle e_k$
    $\displaystyle J_k$ is the current.

    $\displaystyle v_kJ_k=(e_a-e_b)J_{ab}$
    $\displaystyle v_kJ_k=\frac{1}{2}[(e_b-e_a)J_{ab}+(e_a-e_b)J_{ab}]$
    $\displaystyle n_t$ is the number of nodes.[/tex]
    $\displaystyle B$ is the number of branches.[/tex]
    $\displaystyle \sum_{k}^{B}v_kJ_k=\frac{1}{2}\sum_{a=1}^{n_t}\sum _{b=1}^{n_t}(e_a-e_b)J_{ab}$
    each J that does not exist in the graph will be zero.
    $\displaystyle \sum_{k}^{B}v_kJ_k=\frac{1}{2}\sum_{a=1}^{n_t}e_a\ sum_{b=1}^{n_t}J_{ab}-\frac{1}{2}\sum_{a=1}^{n_t}e_b\sum_{b=1}^{n_t}J_{a b}=0$

    because by kcl
    $\displaystyle \sum_{b=1}^{n_t}J_{ab}=0$

    my problem iswhen he sums for all nodes
    he uses
    $\displaystyle \sum\sum$ sign which by me represents multiplication
    of the sums

    why not $\displaystyle \sum+\sum$,thus we can know that ist the sum of many similar equations.

    but how he did it doesnt represent a sum
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Haven's Avatar
    Jul 2009
    The double sum in this case represents a nested sum (if you're familiar with programming, it's like a nested for loop).
    In your problem:
    $\displaystyle \frac{1}{2}\sum_{a=1}^{n_t}\sum_{b=1}^{n_t}(e_a-e_b)J_{ab}$
    means for every iteration of a, we go through all $\displaystyle n_t$ iterations of b. I like to think of it as sort of a series exponentiation.

    Formally if we define: $\displaystyle F = \sum_{i=0}^{n} a_{i}$ and $\displaystyle G = \sum_{j=0}^{n} b_{j}$

    $\displaystyle F * G = \sum_{i=0}^{n} a_{i}b_{n-i}$

    $\displaystyle F G = \sum_{i=0}^{n}\sum_{j=0}^{n} a_{i}b_{j}
    Will yield different answers. I'm not sure about the actual concepts, I'm not very well versed in physics, but your prof is using the nested case.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Double angle question help?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jul 18th 2010, 06:09 AM
  2. Double angle question
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Feb 15th 2010, 05:24 AM
  3. basic question about designation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 12th 2009, 02:50 PM
  4. Double Integral Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 11th 2009, 07:47 AM
  5. Double Summation question
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Oct 27th 2008, 11:49 AM

Search Tags

/mathhelpforum @mathhelpforum