Kirchoff’s Laws

Kirchoff’s First Law

“Sum of all currents meeting at a point in the circuit is zero” i.e. ΣI=0
“Sum of all currents flowing towards a point is equal to sum of all currents flowing away from that point”

Ace to convention current flowing towards the point is taken positively and flowing away is taken negatively.

kirchoff's first Law graph representation

I1 + I2 + (-I3) + (-I4) = 0

I1 + I2 = I3 + I4


ΣI = 0

This equation verifies the law of Conservation of Charge.

Related material:

Kirchoff’s Second Law (Voltage Rule)

“Sum of all voltage changes in a clsed circuit or loop is equal to zero”
“The algebraic sum of all voltages for a complete circuit is zero”

Kirchoff’s Second Rule is the verification of the Conservation of Energy.

Practically Applicable Solution of Circuit

  1. Draw the circuit.
  2. The loops should be chosen so that each resistance is included at least once in each loop.
  3. Assume the direction of the current is either clockwise or anti-clockwise. All the current loops should be in the same order.
  4. Write the loop equation:
    • The voltage across each resistor is negative.
    • Its the direction of flow of current due to the battery (conventional current) and the direction of loop current is parallel then the EMF (electromotive force) of the battery is taken to be positive otherwise negative.
  5. Finally, solve the equations for each loop simultaneously for unknown quantities.


kirchoffs second law graph representation

E1 – E2 – IR1 – IR2 =0



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