i cant understand sum points in this TELEGAN law proof..

**transgalactic** · 22nd November 2009 10:39 AM

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 $e_k$
$J_k$ is the current.

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

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

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

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

but how he did it doesnt represent a sum

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