Infinity Science study: Kirchhoff's Laws(KVL and KCL) and Sign Convention

Kirchhoff’s Laws:

  

Some time we encounter circuit where simplification by series and parallel combination is impossible. Consequently, Ohm’s law cannot be applied to solve such circuits. Kirchhoff gave two laws to solve such complex circuits, namely:

1.  Kirchhoff’s Current Law (KCL)    2.  Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Current Law (KCL): 

The algebraic sum of the currents meeting at a junction in an electric circuit is zero.

An algebraic sum in which the sign of the quantity is taken into account. For example, consider four conductors carrying currents I1, I2, I3 and I4 and meeting at appoint O as positive, the currents flowing away from point O will be assigned negative sign. Thus, applying Kirchhoff’s current law to the junction O in figure (1), we have,

   (I1) + (I4) + (-I2) + (-I3) = 0

                       I1 + I4 = I2 + I3

i.e.,    Sum of incoming current = sum of outgoing currents

Hence, Kirchhoff’s current law may also started as under:

The sum of current flowing towards any junction in an electrical circuit is equal to the sum currents flowing away from the junction.

Note: Kirchhoff’s current law also called junction rule.

Kirchhoff’s Voltage Law (KVL):

This laws relate to e.m.fs and voltage drops in a closed circuit or loop and may be started as under:

 In any closed electrical circuit or mesh, the all algebraic sum of all the electromotive forces (e.m.fs) And the voltage drops in resistor is equal to zero, i.e.,

In any closed circuit or mesh,

Algebraic sum all e.m.fs + Algebraic sum of voltage drops = 0

The validity of Kirchhoff’s voltage law can be easily established by referring to the loop ABCDA show in figure (2). If we start from any point (say point A) in this closed circuit and go back to the point(i.e., point A) after going round the circuit, the there is no increase or decrease in potential. This means the algebraic sum of the e.m.fs of all the sources (here only one e.m.f. source is consider) met on the way plus the algebraic sum of the voltage drops in resistances must be zero. Kirchhoff’s voltage law based on the law of *conservation of energy, i.e., net change in the energy of a charge after completing the closed path is zero.

Note: Kirchhoff’s voltage law is also called loop rule.
Sign convention:

While applying Kirchhoff’s voltage law to a close circuit, algebraic sum are considered. Therefore, it is very important to assign proper signs to e.m.fs and voltage drops in the closed circuit. The flowing sign convention may be followed:

A rise of potential should be considered positive and fall in potential should be considered negative.

Thus in figure (3a) as go from A to B (i.e., from negative terminal of the cell to the positive terminal), there is a rise in potential.

In figure (3b) as we go from A to B, there is a rise in potential.

In figure (3c) as we go from C to D, there is a fall in potential.

In figure (3d) as we from C to D, there is again a fall in potential.