Question

19. State Joule's law of heating. Derive the formula for the Heat produced due to current flowing in a
conductor.

Answer 1

Answer: hello

heating effect produced by an electric current, I through a conductor of resistance, R for a time, t is given by H = I2Rt. This equation is called the Joule's equation of electrical heating. b)The resistance of the filament used in the bulb. A 2.5 kW immersion heater is used to heat water.

Explanation:Introduction

When current flows through a conductor, heat energy is generated in the conductor. The heating effect of an electric current depends on three factors:

The resistance, R of the conductor. A higher resistance produces more heat.

The time, t for which current flows. The longer the time the larger the amount of heat produced

The amount of current, I. the higher the current the larger the amount of heat generated.

Hence the heating effect produced by an electric current, I through a conductor of resistance, R for a time, t is given by H = I2Rt. This equation is called the Joule’s equation of electrical heating.

Electrical energy and power

The work done in pushing a charge round an electrical circuit is given by w.d = VIt

So that power, P = w.d /t = VI

The electrical power consumed by an electrical appliance is given by P = VI = I2R = V2/R

Example

An electrical bulb is labeled 100W, 240V. Calculate:

a)The current through the filament when the bulb works normally

b)The resistance of the filament used in the bulb.

Solution

I = P/V = 100/240 = 0.4167A

R = P/I2 = 100/ 0.41672 = 576.04Ω or R = V2/P =2402/100 = 576Ω

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Answer 2

Answer:

Joule's law of heating states that the power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the electric current passing through the conductor.

That is =>

Joule's law of heating states that when a current 'I ' passes through a conductor of resistance 'R' for time 't' then the heat developed in the conductor is equal to the product of the square of the current, the resistance and time.

We know that the heating impact of electric current when it travels in a circuit is because of collision among electrons of wire. Specifically, what is the amount of heat generated during the flow of current through a wire and what are the parameters and conditions it is based upon. To answer all these questions, Joule gave a formula that describes this phenomenon precisely and called as Joule’s Law.

The heat that is generated because of the current flow in an electric wire is described in Joules. The mathematical expression of Joule’s law is as explained below.

The joule’s first law shows the relationship between heat produced by a flowing electric current through a conductor.

Q = I^2Rt

Where,

• Q indicates the amount of heat

Then,

Q = H (heat) = W (Workdone)

• I show electric current

• R is the amount of electric resistance in the conductor

• t denotes time (in seconds)

The amount of generated heat is proportional to wire’s electrical resistance when the current in the circuit and the flow of current is not changed.

The amount of generated heat in a conductor carrying current is proportional to the square of the current flow through the circuit when the electrical resistance and current supply is constant.

The amount of heat produced because of the current flow is proportional to the time of flow when the resistance and current flow is kept constant.

When all three situations are put together, the resulting equation is expressed as,

H = I^2Rt

We know that, by ohm's law,

R = V/I

=> I = V / R

=> V = IR

And, P = VI

By applying ohm's law in the Joule's Law of heating, we get,

=> H / Q / W = I^2Rt = VIt = Pt = (V^2/R)×t

Hence, we derive the equations of Joule's Law of Heating.

'A piece of Supplementary Counsel' :-

• Ohm's Law = Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

• Power = Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Electric power is usually produced by electric generators, but can also be supplied by sources such as electric batteries.

• Electrical Energy = Electrical energy is energy derived from electric potential energy or kinetic energy. When used loosely, electrical energy refers to energy that has been converted from electric potential energy. This is expressed in Joule.