# Illustration Of Ohm's Law And Kirchhoff's Laws

It is the student’s mentality to think that electrical engineering is difficult. Electrical laws are basic building blocks for all the subjects of electrical engineering. Staring from Ohm’s law, every law is important in electrical engineering. This article introduces the important laws of electrical engineering and also gives the idea of apply them correctly.

## Ohm's law

Ohm's law is defined as the current flowing through the circuit is directly proportional to the voltage applied across the circuit at constant room temperature.

i.e. I a V or

**I=V/R ………(i)**

1/R is the constant of proportionality and called as conductance and its unit is mho or Siemens.

Ohm's law can also be given as V a I or

**V=IR….. (ii)**

'R' is the constant known as resistance of the circuit. It is defined as the opposition offered by the circuit for the flow of current. Its unit is ohm (?).

Fig.(i)

In the fig(i)

'R' is resistance of the circuit.

'V' is voltage applied across the circuit.

'I' is current flowing through the resistor.

Ohm's law is applicable to both AC and DC circuits, but can not be applied under the conditions of variable temperature and to any semiconductor devices.

## Kirchhoff's laws:

**Kirchhoff's Current law (KCL):**

This fundamental law results from the conservation of charge. It states that at any junction or node algebraic sum of currents entering the node is equal to algebraic sum of currents leaving the node. In general the summation of currents meeting at the junction is always zero.

i.e. ? I = 0

Consider the network shown below.

Fig(ii)

From the circuit shown KCL is written as

I1+I2=I3+I4 or I1+I2-I3-I4=0

**Kirchhoff's voltage law (KVL) :**

It states that in any network, the algebraic sum of the voltage drops across the circuit elements of any closed path or loop is equal to the algebraic sum of the e.m.f s in the path. In other words "the algebraic sum of all the branch voltages, around any closed path or closed loop is always zero."

i.e. ? V = 0

This law can be applied to both AC and DC circuits.

Fig(iii)

Before proceeding with the illustration of the law, let us know about the concept of potential rise and potential drop. Consider a resistor in which current I is flowing from end 'a' to end 'b'. Polarities are as shown. '+' sign shown at end 'a' indicates that it is at higher potential and end 'b' is at lower potential. From 'a' to 'b' there is drop in the voltage and is indicated by '-'sign. Hence the drop from 'a' to 'b' is –IR. Without changing the direction of the current, voltage measured from 'b' to 'a' is voltage rise and indicated by '+' sign and hence drop from 'b' to 'a' is +IR. This concept is very important to understand the application of KVL.

Consider the circuit shown below.

Fig(iv)

In this cirucit there are two loops, 3resistors and one voltage source. Assume the directions of currents arbitrarily.

Applying KVL to the loops

i)abefa

V1-I1R1-I3R3=0 or V1=I1R1+I3R3

I3=I1-I2

ii)bcdeb

-I2R2+I3R3=0

iii)abcdefa (Though there are three loops, abcdefa also forms the outer loop which can also be considered)

V1-I1R1-I2R2=0 or V1=I1R1+I2R2

Consider one more example where two voltage sources are included.

Fig(v)

Applying KVL to the loops

i)abefa

V1-I1R1-I2R2-V2=0 or V1-V2=I1R1+I2R2

I3=I1-I2

ii)bcdeb

-I2R2 -V2+I3R3=0 or V2= I3R3-I2R2

iii)abcdefa

V1-I1R1-I2R2-V2=0

For the same circuit with two voltage sources, directions of currents can also be assumed as follows.

Fig(vi)

Hence, the corresponding KVL equations are written as

i)abefa

V1-I1R1-I3R3=0 or V1=I1R1+I3R3

I3=I1+I2

ii)bcdeb

I2R2-V2+I3R3=0

iii)abcdefa

V1-I1R1+I2R2-V2=0

**Points to remember:**

Naming and following the order of the loop is very important aspect to avoid doing mistakes. For ex: if name of the loop is 'abcda' then starting from noe 'a' you have to proceed as 'a' to 'b', then cda. Remember, 'abcd' is not the loop. Loop should end with the starting node. i.e. 'a' in this case. Once the equtaions are written it can be simplified according to convenience. Number of unkown currents are equal to number of loop equations. For the circuits shown above, out of the three euations written, two are suffiecient to solve for the unknown circuit currents.

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