Kirchhoff’s Laws
Kirchhoff’s laws are particularly useful
- in determining the equivalent resistance of a complicated network of conductors and
- for calculating the currents flowing in various conductors.
Kirchhoff’s Current Law (KCL)
This law is also known as Kirchhoff’s point law or Kirchhoff’s First law. It states that “In any electrical network, the algebraic sum of the current meeting at a point (or junction) is zero.” It means that the total current leaving a junction is equal to the total current entering that junction.
In Fig 1, some condutors have current leading to node whereas some have current leaving away from the node. Assuming the incoming current to be positive and outgoing current negative, we get,
I1 + I2+(-I3)+(-I4)+(-I5) = 0
or, I1 + I2 = I3 + I4 + I5
ie. incoming current = outgoing current
Kirchhoff’s Voltage Law (KVL)
This law is also known as Kirchhoff’s mesh law or Kirchhoff’s second law. It states that “the algebraic sum of the product of current and resistances in each of the conductor in any closed loop path (or mesh) in a network plus the algebraic sum of the e.m.f. in that path is zero.”
Mathematically,
∑IR +∑ emf =0
Using KVL in fig 2,
E1 + V1 – V2 – E2 = 0
or, E1 + V1 = E2 +V2