Question
Download Solution PDFConsider the following two statements -
1. Kirchhoff's junction law follows from conservation of charge.
2. Kirchhoff's loop law follows from conservative nature of electric field.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFKirchoff's Current Law (KCL)
According to KCL, the algebraic current at a node is always zero.
ΣI = 0
\(-I_1-I_2-I_3+I_4+I_5=0\)
\(-{dq_1\over dt}-{dq_2\over dt}-{dq_3\over dt}+{dq_4\over dt}+{dq_5\over dt}=0\)
Hence, KCL is based on the conservation of charge principle.
Kirchoff's Voltage Law (KVL)
According to KVL, the algebraic sum of the voltages in a closed loop is always zero.
ΣV = 0
\(-V_1+V_2+V_3+V_4=0\)
\(\int E.dl=0\)
A conservative field means that the work done by the electric field on a charge depends only on the starting and ending points, not on the path taken.
For a closed loop, the starting and ending points are the same, so the total work done (or total potential difference) is zero.
Hence, KCL is based on the conservation of electric field.
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