Kirchhoff’s Laws – Kirchhoff’s Current and Kirchhoff’s Voltage Laws

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Kirchhoff’s Laws

Kirchoff’s current law or point law (KCL)

Statement:-

In any electrical network, the algebraic sum of the currents
meeting at a point is zero.
Σ I = 0 ……………………at a junction or node

Assumption:-

Incoming current = positive
Outgoing current = negative

Kirchoff’s voltage law or mesh law (KVL)

Statement:-

The algebraic sum of the products of currents and resistances in
each of the conductors in any closed path (or mesh) in a network plus the
algebraic sum of the emfs in that path is zero.
Σ IR +Σemf = 0 …………………………..round the mesh

Assumption:-

  1. Rise in voltage (If we go from negative terminal of the battery to positive terminal) = positive

  2. Fall in voltage (If we go from positive terminal of the battery to negative terminal) = negative

  3. If we go through the resistor in the same direction as current then there is a fall in potential. Hence this voltage is taken as negative.

  4. If we go through the resistor against the direction of current then there is a rise in potential. Hence this voltage drop is taken as positive.

Example:-

Write the loop equation for the given circuit below

Solution:

Apply KVL to the loop,

 

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