Question

How is the Kirchoff Law a consequence of the conservation of charge and energy?

Answer 1

First law states that at the junction net algabric sum of currents is zero means total charge coming to the junction is equal to total charge going out from junction this clearly support to conservation of charge.

Second low states that summation of counteneous potentials

in a closed mesh is equal to zero. Which means total work done in caring a charge via closed loop start to a point and at the returning at same point via a closed loop is zero. Here we can assume net displacement of charge is zero in conservative electric field.