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