ByAPSEEE

Kirchhoff’s Law are used to solve those networks or circuit where ohms law is may not be readily solved that circuit. Gustav Kirchhoff’s, a German Scientist, summed up his findings in a set of two laws which are called Kirchhoff’s Law. Resistance of a complicated circuits and for calculating the currents flowing in the various branches of circuits or networks. The two laws are Kirchhoff’s current law and Kirchhoff’s voltage law.

**Kirchhoff’s Current Law (KCL)**

This law relates the currents flowing through the circuit that is why this law is called Kirchhoff’s current law. This law is also known as Kirchhoff’s point law.

This law states that, in any electrical network, the algebraic sum of the currents meeting at a junction or node is always zero.

Lets us consider a case in which few conductors meeting at a junction or point A, where some conductors have current entering to the point and some conductors have currents leaving out the point. Assuming currents entering to the point to be positive while the outgoing currents are negative.

We have,

I_{1}-I_{2}-I_{3}+I_{4}+I_{5}=0

I_{1}+I_{4}+I_{5}= I_{2}+I_{3}

Incoming Currents = outgoing Currents

In other words, we can say that incoming current is equal to outgoing current.

**Kirchhoff’s Voltage Law (KVL)**

This law relates the voltages in a closed circuit of an electrical network. It is also known as Kirchhoff’s mesh law.

Kirchhoff’s voltage law states that the algebraic sum of product of current and resistance in a closed network is equal to the algebraic sum of EMFs in that closed path that is in a closed circuit.

V_{1}+V_{2 }= IR_{1}+IR_{2}

∑V = ∑IR = 0 or ∑IR = ∑V

In other way we can say that, in a closed circuit or mesh, the algebraic sum of all the EMFs plus the algebraic sum of products of currents and resistances is zero.

∑V + ∑IR = 0

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ByAPSEEE

Ohm’s Law gives the relation between voltage and current. Whenever an electric potential difference (V) is applied across two points of the conductor, the current (I) flows through it. The flow of current is opposed by the resistance (R) of the conductor. The value of resistance (R) will remain constant for all value of voltages and currents. This relation was expressed first of all by a German Scientist, George Simon Ohm that is why it is called Ohm’s Law.

Ohm’s Law states that current flowing between to applied voltage or points of conductor is directly proportional to applied voltage or potential difference between two points of conductor. Provided the temperature and other physical conditions of the conductor do not change.

Mathematically,

In other words, Ohm’s Law can also be defined as,

The ratio of potential difference across any two points of a conductor to the current flowing through the conductor is always constant. This constant is called resistance (R).

The linear relationship (I α V) does not apply to all non-metallic conductors. For example for silicon carbide, the relationship is given by V = kI^{X} where k and x being constants; x is always less than unity.

Limitations of Ohm’s Law

- Ohm’s Law is not applied to non-linear resistors like vacuum radio value, semiconductors etc.
- It is not applied to arc lamps.
- Electrolytes where enomous gases are produced on either electrode.
- It is not applied to unilateral elements.

Applications of Ohm’s Law

Ohm’s Law applies to linear circuits to find resistance, current and voltages.

ByAPSEEE

It is the property of a substance which restricts the flow of electric current.

We know that current is the flow of electrons, hence resistance is an opposition to the flow of electrons. This opposition occurs due to the presence of large number atoms and molecules.

When current flows through a substance, the free electrons move through the material and collide with atoms and molecules. These collisions cause the electrons to lose some of their energy and it also offer opposition to the flow of electrons. The atomic structure of the substance decides the extent of the opposition.

Silver, copper and aluminum offer least resistance to flow of current. Tungsten, Nichrome offer very high resistance to flow of current.

The unit of Resistance is ohm** (****Ω****)**, denoted by **R**.

**Factor Affecting Resistance**

Resistance of a conductor depends upon the following factors

**Length**

Resistance of conductor is directly proportional to the length of the conductor. Greater the length, greater the resistance and vice versa.

**R α l——————– (i)**

**Area of Cross Section**

Resistance of conductor is inversely proportional to the area of cross section of the conductor. Greater the area of cross section, lesser the resistance and vice versa.

**R α 1/a——————– (ii) **

**Nature of Material**

Resistance of the conductor depends upon the nature of the composition of the material of which the conductor is made up. Difference substances have different atomic structures and therefore, offer different resistances for the same length and area of cross section.

**Temperature**

The resistance of the conductor depends upon the temperature of the conductor. The resistance of the conductor increases with increase in temperature.

From equation (i) and (ii), we get

**R α l**

**R α 1/a**

**R α l/a**

**R = ρ l/a**

Where P (Rho) is constant of proportionality and it’s called resistivity or specific resistance of the material. P (Rho) refers to the nature of material.

**Effect of Temperature on Resistance**

**For Metals**

The resistance of metals increases with increase in temperature. The graph plotted between temperature and resistance is straight line. The metals have positive temperature co-efficient of resistance.

**For Alloys**

The resistance of alloys increases with the increase in temperature but the increase is very small and irregular.

**For insulators, electrolytes, semiconductor etc**

The resistance of insulators, electrolytes and semiconductors decreases with the rise in temperature. These materials have negative temperature co-efficient of resistance.

ByAPSEEE

The number of free electrons are available in conductors and semiconductors. In the absence of electric field, these free electrons moves in random directions shown in figure.

When an electric field is applied to the conductors and semiconductors, the free electrons start moving in a particular direction and it constitutes an electric current.

**Definition of electric current**

The rate of flow of electric charge through any section of wire is called electric current. The electric current flows if the circuit is closed.

**(The SI unit of electric current is Ampere. It is denoted by I)**

Conventional current and electron current

**Conventional current**

The current flows from the positive terminal of the battery to the negative terminal of the battery are called conventional current.

**Electron Current**

The current flows from negative terminal of the battery to the positive terminal of the battery is called electron current. In metals, current is caused by electrons and such kind of current is known as electric current.

**Types of Electric Current**

An electric current is divided into AC current and DC current.

**AC Current **

AC stands for Alternating Current. Alternating Current changes its direction and magnitude w.r.t. time or at regular intervals.

- AC Current can be stepped up or stepped down.
- AC Current can be generated at higher voltage.

**DC Current**

DC stands for direct current. Direct current has constant magnitude and direction.

- DC Current cannot be stepped up or stepped down.
- DC Current cannot be generated at high voltages due to commutation problems.

**Properties of Electric Current**

**Heating Properties**

When electric current flows through a high resistive material heat is produced. This property of electric current is used in various heating devices, such as stoves, radiators, water heaters, welding, electric lamps, arc furnaces etc.

**Magnetic Properties**

When electric current passes through a coil, a magnetic field is produced. Magnetic properties of an electric current are utilized in various electrical machines. Such as electric generators, electric motors, relays etc.

**Electrochemical Properties**

When electric current passes through an electrolyte, chemical action takes place. The electro-chemical properties of an electric current is utilized in electro-chemical industries for various applications such a electro-plating, electrolytic refining, electro-deposition etc.