Ohm’s law
establishes a relationship between voltage and current. It was one of the
simplest equations developed by George Simon ohm. But, ohm’s law alone could
not be used to analyze large and complex circuits. Later on, Gustav Robert
Kirchhoff (1824-1877) formed the two fundamental laws which are used in writing
the circuit equations.
The laws
developed by him depend neither on the nature of elements of the circuit nor
the topology of the elements (Topology means the way the elements are connected).
WHAT ARE THE TWO LAWS?
They are:
- Kirchhoff’s current law (KCL)
- Kirchhoff’s voltage law (KVL)
KIRCHHOFF’S CURRENT LAW –
It states
that the algebraic sum of the currents flowing across a junction or node is
equal to zero. This implies that for the figure given below - ${{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}+{{I}_{5}}=0$
 |
| CURRENTS COMING TO A JUNCTION |
KCL is based
on the principle of law of conservation of charge. This is because the amount
of charge entering a junction must be equal to the amount of charge leaving a
junction; since charges cannot accumulate at a point.
Mathematically,
if there are b no. of branches meeting at a node or junction, then
\[\sum\limits_{n=1}^{b}{{{I}_{n}}}=0\]
KIRCHHOFF’S VOLTAGE LAW –
It states
that the algebraic sum of the voltages around a closed loop or path or circuit
is zero. For a closed loop having n elements,
\[\sum\limits_{i=1}^{n}{{{V}_{n}}=0}\]
KVL is based
on the law of conservation of energy. This means that the charges travelling
around a closed loop just transfer energy from one element to another, but they
do not receive or store any energy themselves. They just transfer the energy.
HOW TO APPLY KCL TO A CIRCUIT?
Consider a
node A of the circuit given below:
Then KCL
equation for this circuit is written as:
${{I}_{1}}={{I}_{2}}+{{I}_{3}}+{{I}_{4}}+{{I}_{5}}$
The current
entering the node is taken to be positive in the equation, while the currents
leaving the node are taken to be negative. There is no hard and fast rule so as
to determine what sign is to be taken for a current. The point is – if you
assume the sign of an entering current to be positive and leaving current to be
negative, then follow the same criteria for that particular circuit OR
vice-versa.
HOW TO APPLY KVL TO A CIRCUIT?
Consider the
circuit given below:
As the circuit is open at terminals a-b; no current will flow in the arms a and b. Otherwise you can also see that no closed loop is formed, so we cannot apply KVL here. But the loop on the left side is a closed loop. Assuming current to be in clockwise direction, the equation is written as –
As the circuit is open at terminals a-b; no current will flow in the arms a and b. Otherwise you can also see that no closed loop is formed, so we cannot apply KVL here. But the loop on the left side is a closed loop. Assuming current to be in clockwise direction, the equation is written as –
\[I{{R}_{1}}+I{{R}_{2}}-V=0\]
Or
\[V=I{{R}_{1}}+I{{R}_{2}}=I({{R}_{1}}+{{R}_{2}})\]
BUT HOW DO
WE OBTAIN THIS EQUATION?
This equation can be obtained by following these simple steps:
This equation can be obtained by following these simple steps:
- Consider any loop in a circuit and assume the current to be in clockwise or anti-clockwise direction. Generally, the direction of current is inferred by seeing the positive terminal of a higher value of voltage source. Because current is supposed to be coming out of the positive terminal of the source.
- Multiply the assumed current variable with the values of the elements which you encounter in your path and write the equation in terms of the sum of these multiplications obtained from each of the element.
- For writing the value of voltage source in your path; write positive sign if you encounter positive terminal first and write negative sign if you encounter negative terminal first.
NOTE:
As the
equation to be written is a sum of voltages, therefore you need not multiply
the current variable with voltage sources.
Only
multiply the values of circuit elements namely resistors, inductors and
capacitors with current variable.
KCL and KVL
form the basic laws for analyzing the circuit. Learning their application to
circuits is of immense importance to every electrical engineering student or
aspirant. Further, there are more circuit theorems in circuit theory which help
to solve circuits. But their application requires the understanding of KCL and
KVL.
