transgalactic
Banned
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)
[latex][/latex]
and decide that the voltage on that node to be zero.
we designate the voltages on the nodes to be [latex]e_k[/latex]
[latex]J_k[/latex] is the current.
[latex]v_kJ_k=(e_a-e_b)J_{ab}[/latex]
[latex]v_kJ_k=\frac{1}{2}[(e_b-e_a)J_{ab}+(e_a-e_b)J_{ab}][/latex]
[latex]n_t[/latex] is the number of nodes.[/latex]
[latex]B[/latex] is the number of branches.[/latex]
[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}[/latex]
each J that does not exist in the graph will be zero.
[latex]\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_{ab}=0[/latex]
because by kcl
[latex]\sum_{b=1}^{n_t}J_{ab}=0[/latex]
my problem iswhen he sums for all nodes
he uses
[latex]\sum\sum[/latex] sign which by me represents multiplication
of the sums
why not [latex]\sum+\sum[/latex],thus we can know that ist the sum of many similar equations.
but how he did it doesnt represent a sum
my prof proved lik this:
we choose a node (a point where more then one currents come together)
[latex][/latex]
and decide that the voltage on that node to be zero.
we designate the voltages on the nodes to be [latex]e_k[/latex]
[latex]J_k[/latex] is the current.
[latex]v_kJ_k=(e_a-e_b)J_{ab}[/latex]
[latex]v_kJ_k=\frac{1}{2}[(e_b-e_a)J_{ab}+(e_a-e_b)J_{ab}][/latex]
[latex]n_t[/latex] is the number of nodes.[/latex]
[latex]B[/latex] is the number of branches.[/latex]
[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}[/latex]
each J that does not exist in the graph will be zero.
[latex]\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_{ab}=0[/latex]
because by kcl
[latex]\sum_{b=1}^{n_t}J_{ab}=0[/latex]
my problem iswhen he sums for all nodes
he uses
[latex]\sum\sum[/latex] sign which by me represents multiplication
of the sums
why not [latex]\sum+\sum[/latex],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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