What is Joule’s Law?
The amount of heat that is produced within an electric wire due to the flow of current is expressed in the unit of Joules. When the current flows through the wire there is a collision between electrons and atoms of the wire which leads to the generation of heat. Joule’s Law states that when a current flows in a conductor the amount of heat generated is proportional to current, resistance, and time in the current flowing. Let us have a look at the concept behind the joule’s law.
Mathematical Representation of Joule’s Law
When in a current conducting wire the time of the flowing of current and the resistance of the wire is constant, the amount of heat produced and the square of the amount of current flowing the wire are proportional to each other.
Equation 1 : \[H \alpha i^{2}\] (Where R and T are Constant)
When in a current conducting wire the time of the flowing of current and the current of the wire are constant, the amount of heat produced and the amount of electrical resistance of the wire are proportional to each other.
Equation 2: \[H \alpha R\] (Where R and T are Constant)
When in a current conducting wire the amount of the electrical resistance and the amount of current are constant, the heat produced and the time of current flowing are proportional to each other.
Equation 3: \[H \alpha t\] (Where R and i are Constant)
Formula of Heat
When equations 1, 2, and 3 are merged, the resulting formula is-
\[H \alpha i^{2}. Rt\] (i, R, and t are variables)
\[H = \frac{1}{J}.i^{2}RT\] (where J is a Joule’s Constant)
The joule’s constant J is defined as the number of work units that furnishes one unit of heat when converted completely into heat.
The value of J= 4.2 joules/cal.
\[H = \frac{1}{J}.i^{2}RT\]
\[H = \frac{i^{2}Rt Joules}{\frac{4.2 Joules}{cal}}\]
= \[ \frac{i^{2}Rt}{4.2 Joules}\]
= \[ \frac{i^{2}Rt}{4.2 Joules}\]
= \[0.24 i^{2} Rt cal\]
According to Joule’s law
\[I^{2} Rt\] = work done in joules when through a resistor of R ohmsi Ampere of current is maintained for t seconds.
\[H = 0.24 Vit cal = 0.24\frac{v^{2}}{R}cal (V = iR)\]
Electrical Power
The rate at which the work is done in an electric circuit in order to maintain the steady current is known as the electrical power of that circuit. It can also be stated as the rate at which the electrical energy is converted into other forms of energy. The SI unit of electrical power in watts W.
\[P = \frac{w}{t} = \frac{I^{2}Rt}{t}\]
\[P = I^{2}R = IV = \frac{V^{2}}{R}\]
FAQs on Joule's Law
1. What is Joule's law of heating in simple terms?
Joule's law of heating states that when an electric current flows through a conductor, it generates heat. The amount of heat produced is directly proportional to the square of the current, the resistance of the conductor, and the duration for which the current flows. Essentially, a stronger current or a higher resistance will produce more heat over time.
2. What is the mathematical formula used to calculate the heat produced by an electric current?
The formula for Joule's law of heating is given by:
H = I²RT
Where:
- H is the amount of heat generated (in Joules).
- I is the electric current flowing through the conductor (in Amperes).
- R is the electrical resistance of the conductor (in Ohms).
- T is the time for which the current flows (in seconds).
3. What are some common examples of Joule's law in our daily lives?
Joule's law has many practical applications that we use every day. Some common examples include:
- Electric Heaters and Stoves: These use heating elements with high resistance to produce heat for warmth or cooking.
- Incandescent Light Bulbs: The filament inside the bulb heats up to such a high temperature that it glows, producing light.
- Electric Fuses: A safety device with a wire that melts and breaks the circuit if the current becomes dangerously high, preventing damage to appliances.
- Electric Toasters and Irons: These use the heating effect to toast bread or press clothes.
4. Why does a conductor heat up when electric current passes through it?
A conductor heats up because the flowing electrons, which make up the electric current, collide with the atoms and ions within the conductor. These collisions transfer kinetic energy from the electrons to the atoms, causing them to vibrate more rapidly. This increased vibration of atoms is what we experience as an increase in temperature, or heat.
5. What is the difference between a Joule and a Watt?
The main difference lies in what they measure. A Joule (J) is a unit of energy, representing the total amount of work done or heat generated. A Watt (W), on the other hand, is a unit of power, which is the rate at which energy is used or generated. In simple terms, power tells you how fast energy is being used. One Watt is equal to one Joule per second (1 W = 1 J/s).
6. Why are materials like Nichrome used for heating elements instead of a good conductor like copper?
Heating elements use materials like Nichrome (an alloy of nickel and chromium) instead of copper for two main reasons:
- High Resistance: Nichrome has a much higher electrical resistance than copper. According to Joule's law (H = I²RT), a higher resistance (R) produces significantly more heat for the same amount of current.
- High Melting Point: Nichrome can withstand very high temperatures without melting or oxidising (rusting) easily, making it durable and effective for repeated heating. Copper would melt at the temperatures required for a toaster or heater.
7. Is the heating effect of current always useful? When is it considered a drawback?
No, the heating effect is not always useful. While it is desired in devices like heaters and toasters, it is a major drawback in many other electrical systems. For example, in devices like computers, transformers, and motors, the heat generated is a form of wasted energy. This unwanted heat can reduce the efficiency of the device and may even cause damage to its components if not properly managed with cooling fans or heat sinks.
8. How does Joule's law explain why electricity is transmitted at very high voltages?
To deliver a certain amount of power (P = VI), we can either use a high voltage (V) and low current (I), or a low voltage and high current. According to Joule's law, the energy lost as heat in the transmission wires is proportional to the square of the current (I²). By using very high voltages for transmission, the required current is kept very low. This significantly reduces the amount of energy lost as heat in the power lines, making the transmission process much more efficient over long distances.
