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In any electric circuit, if i1 and i3 are incoming currents and i2 and i4 are outgoing currents from a node, then according to KCL which is the correct answer?
i1+i3=i2+i4
i1+i2=i3+i4
i4-i1=i2+i3
i1-i2=i3-i4
i1+i3=i2+i4
Kirchhoff's Current Law (KCL) states that the algebraic sum of currents meeting at a node (junction) is zero. Essentially, this means the total current entering a node must equal the total current leaving the node, satisfying the law of conservation of charge.
Kirchhoff's Current Law (KCL) states that the algebraic sum of currents meeting at a node (junction) is zero. Essentially, this means the total current entering a node must equal the total current leaving the node, satisfying the law of conservation of charge.
тИСk=1nтАЛIkтАЛ=0 тАФ General statement of KCL
тИСIenteringтАЛ=тИСIleavingтАЛ тАФ Practical application of KCL
The principle is based on the law of conservation of charge, which dictates that electric charge cannot be created or destroyed at a point. Therefore, if iinтАЛ and ioutтАЛ represent the currents at a node, the continuity of charge flow requires тИСiinтАЛ=тИСioutтАЛ.
KCL is derived from the principle of conservation of charge.
A node is a point where two or more circuit elements meet.
KCL is applicable to both DC and AC circuits.
In AC circuits, the currents must be summed as phasors.
Simplifies circuit analysis for multi-loop networks.
Provides a systematic method to solve for unknown nodal voltages (Nodal Analysis).
Can become algebraically intensive for circuits with a very large number of nodes.
Requires proper sign convention (usually incoming as positive, outgoing as negative).
Nodal Analysis of complex electronic circuits.
Calculation of currents in parallel distribution networks.
Option B (i1тАЛ+i2тАЛ=i3тАЛ+i4тАЛ) implies i1тАЛ and i2тАЛ are both incoming/outgoing, which contradicts the problem statement.
Option C and D are algebraic rearrangements that do not satisfy the fundamental balance of inward and outward flow.
A is correct тАФ According to KCL, the sum of incoming currents must equal the sum of outgoing currents, represented as i1тАЛ+i3тАЛ=i2тАЛ+i4тАЛ.
Always remember that KCL relates to charge conservation, while Kirchhoff's Voltage Law (KVL) relates to energy conservation.
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