Current

Show that in an electric circuit when a current gets divided into a number of branches it does so in such a way that the heating effect is minimum?

1 Answers

ya..nice question

u can do it for a current I splitting into two parts and going to say R1 (x current) and R2( I-x current)

R1 and R2 are resistances..hmm now do one thing

P(x) = x^2(R1) + (I-x)^2 (R2)

differentiate to get the minimum, => x= R2(I)/ (R1+R2)

and what u see??? u get the expected value of x( current gets divided in the two branches in inverse ratio of R1 and R2 :) )

this completes the proof

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