Write and explain kirchhoff's first law (junction law).

Explanation

`rArr` Statement : At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving junction.
`rArr` This applies equally well it instead of a junction of serval lines, we consider point on line.

`rArr` In figure current coming out of. a. is `I_(1) + I_(2)` and current coming toward junction is `I_(3)` .
`therefore` From Kirchhoff.s law,
`I_(3) = I_(1) + I_(2)`
`rArr` Proof of this rule follows from the fact that when current are steady there is no accumulation of charges at junction or at any point in a line. That means charge is conserved.
Whatever amount of charge enter in given time at a point or junction similar amount of charge will flow out through that point or junction in same time.
In figure shown `I_(1) ` current enter at point h and same current `I_(1)` flow out through that point means charge is conserved at point h.
`rArr` Kirchhoff.s first law is based on the conservation law of charges.
Kirchoff.s first rule : " The algebraic sum of currents flowing through any junction is equal to zero. "
.O. is a junction of one network `I_(1), I_(2)..... I_(5)` are the electric currents having arbitrary direction.

Suppose `Q_(1), Q_(2) .... Q_(5) ` are charges, for the currents `I_(1), I_(2).... I_(5)` repsectively. Then , `Q_(1) = I_(1) , t, Q_(2) = I_(2) t, ........ Q_(5) = I_(5)t.`
The charges coming to the junction in time t is `Q_(1) + Q_(3)`, while that receding from junction is `Q_(2) + Q_(4) + Q_(s) `.
Accroding to the law of conservation of electric charge.
`Q_(1)+ Q_(3) = Q_(2) + Q_(4) + Q_(5)`
`therefore I_(1) t + I_(3) t = I_(2) t + I_(4) t + I_(5) t ` [ from equ. (1)]
`therefore I_(1) = I_(3) = I_(2) + I_(4) + I_(5)`
`therefore I_(1) - I_(2) + I_(3) - I_(4) - I_(5) = 0 `
`therefore I_(1) + (- I_(2)) + I_(3) + (- I_(4)) + ( - I_(5)) = 0... (2)`
` therefore sum_(i=1)^(5) I_(i) = 0`
Where, i = 1 , 2 ... 5 Krichhoff.s first law.
hence, the algebraic sum of currents meeting at any junction is zero.
here, current coming towards the junction is considered positive and current going out of the junction is considered negative. we can choose reverse convention also .