Kirchoff's point rule is direct consequence of law of conservation of-
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Kirchhoff's voltage law (2nd Law) states that the sum of all voltages around any closed loop in a circuit must equal zero. This is a consequence of charge conservation and also conservation of energy.
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Charge conservation
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According to Kirchoff's point rule the sum of current at any point is always zero.
Now let the outgoing current at any point is positive and incoming current as negative, let the outgoing current at any point is and incoming current at the point is
Then according to Kirchoff's point rule ( here positive sign is for outgoing current and negative sign is for incoming current )
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