Heating Effect of Electric Current and Domestic Wiring

Heating Effect of Electric Current and Domestic Wiring Synopsis

Synopsis

Heat Effect of Electric Current

Suppose when a battery is connected across a conductor, such that current starts flowing from its positive terminal towards the negative terminal because of the large number of free electrons present in a conductor.
This is because when the potential difference is applied across the conductor, the electrons start drifting toward the highest electric potential (From lower to higher electric potential).
During this process, electrons undergo collision with positive ions of a conductor as a result the average kinetic energy of atoms increases and we can feel that heat emitted from such conductor.
In simple terms when current flows through a conductor some of the electric energy is converted into heat energy due to the collision of an electron with positive ions of a conductor, as a result, the temperature of the conductor increase.

The heat energy produced because of the flow of current will depend on the following factors:

Current: The amount of heat produced during this process is directly proportional to the square of the amount of current flowing through a conductor.
⇒ Q ∝ I²
Resistance: The amount of heat produced during this process is directly proportional to the resistance offered to current flow because of the collision of free electrons.
⇒ Q ∝ R
Time period: The amount of heat produced during this process is directly proportional to the time period for which the current is allowed to flow through a conductor.
⇒ Q ∝ t

From this, we can conclude that,

⇒ Q ∝ I² Rt

Now by using Ohm’s law (V = IR) we can also modify the above equation as;

$begin mathsize 12px style rightwards double arrow Q space equals space V I t equals V squared over R t end style$

Note: Just like any other energy, heat energy produced because of electric current is also measured in Joules in the S.I system of units.

We see this phenomenon in our day-to-day life and some of the important applications of heat effect due to electric current are:

Electric heater
Electric iron
Incandescent light bulb
Electric fuse

Joule’s law of heating

James Prescott Joule an English physicist, performed series of the experiment through which he was successful in establishing the relation between mechanical work ‘W’ done by a body and quantity of heat produced ‘Q’ because of work done.

i.e., W ∝ Q ⇒ W = J Q

Here J is Joule's constant also known as Joule’s mechanical equivalent of heat and its value is 4.18 J/cal.

⇒ W = JQ

Using this the quantity of heat energy produced according to joules law will be measured in calories as shown below

begin mathsize 12px style therefore Q equals fraction numerator I squared R t over denominator J end fraction equals fraction numerator I squared R t over denominator 4.18 end fraction c a l end style

Electric Power

According to classical mechanics, power is defined as the rate of doing work or the rate of consumption of energy.

i.e.,

begin mathsize 12px style P equals W over t end style

Similarly for electrical energy, the work done per unit time is known as electric power. And power in terms of voltage and current is given as;

begin mathsize 12px style i. e. comma P equals W over t rightwards double arrow P equals V I....... open parentheses because V equals W over Q space a n d space I space equals space Q over t close parentheses end style

Also, by using Ohm’s law the above equation for electric power can be modified as;

begin mathsize 12px style P equals V I equals I squared R equals V squared over R end style

Here, V is the voltage applied and, R is resistance and I is current passing through a conductor.

S.I unit of power is watt it is also measured in Joules/sec.

i.e., 1 Watt (W) = 1 Joule/sec

Also, since horsepower is also one of the units of measurement for power, the relationship between watt and horsepower is given as;

⇒ 1 Horsepower (hp) = 746 W

In our house hold for commercial use the amount of electrical energy consumed per unit time is measured in terms of kilowatt hour (kWh) and its relation in terms of Joules is given as;

1 watt hour (Wh) = 1 watt (W) × 3600 sec …. (∵ 1 hour = 60min × 60 sec)

∴ 1 Wh = 3600 W.s = 3600 J …. (∵ 1 W = 1 J/s)

i.e., 1 kWh = 1000× 1 Wh = 3.6 × 10⁶ J = 3.6 MJ

As we can see in terms of joules the amount of energy is very high (in Mega Joules or 10⁶ J), because of this for commercial application and our simplicity we use kWh as a unit of measure for consumption of electrical energy and it is also known in terms of Unit as mentioned in our electric bills (i.e., 1 Unit = 1 kWh).

Coulomb’s law

According to Coulomb’s law, the force of interaction between two charged particles is directly proportional to the product of two charges and inversely proportional to the square of the distance between them.

begin mathsize 12px style i. e. comma space F space alpha space fraction numerator q subscript 1 q subscript 2 over denominator r squared end fraction rightwards double arrow F space equals space fraction numerator k q subscript 1 q subscript 2 over denominator r squared end fraction end style

Here, k is the proportionality constant also known as Coulomb’s constant, q₁ and q₂ are the magnitude of two-point charges, r is the distance between two charges.

The above equation can also be expressed as;

begin mathsize 12px style F space equals space fraction numerator 1 over denominator 4 straight pi element of subscript 0 end fraction cross times fraction numerator q subscript 1 q subscript 2 over denominator r squared end fraction....... open parentheses because space k space equals fraction numerator 1 over denominator 4 straight pi element of subscript 0 end fraction almost equal to space 9 space cross times space 10 to the power of 9 space k g space m cubed space s to the power of negative 2 end exponent C to the power of negative 2 end exponent space close parentheses end style

Where ϵ₀ is the permittivity of free space and it is given as 8.85 × 10^-12 N^-1m^-2

Domestic Electric Circuit

Standard Colour Coding of Wire

In Indian households, we receive a power supply of standard 220 V and 50 Hz and the main electric power supply is known as the mains.
For all-electric appliances the standard colour code is:
1. Red wire: the wire with red insulation is known as the live wire.
2. Black wire: the wire with black insulation is known as neutral wire.
3. Green wire: the wire with green insulation is known as earth. The earth wire in the wiring is used as a safety measure to prevent the user from getting electrocuted, in case if the metal body comes in constant with the live wire. This earth wire is connected to the earth, which is considered as zero potential. This process is termed earthing.
Hence for our simplicity and to avoid any accidents because of confusion we use standardize colour coding for electrical wiring.
The above-mentioned colour codes for electric wire are according to the old convention (RBG mode) but recently electricians started using a new convention for electrical wiring (BBG mode) in which brown wire is used as a live wire, blue is used for neutral wire and green is used for earthing.
The below figure shows the connection of earth, live and neutral wire for our household.

Electric Fuse

An electric fuse is an important safety device, which is used to protect the circuits in case of any short-circuiting or overload.

Overloading is a phenomenon that may occur when live and neutral wires come in contact with each other because of improper insulation, Voltage fluctuation or due to fault in an appliance.

As a result, the current passing through a circuit increases rapidly and causes a short circuit.

An electric fuse works on the principle of Joule heating, it is made in such a way that the fuse wire melts when the amount of current flowing through it increases by a certain value.

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Heating Effect of Electric Current and Domestic Wiring