20.1 Electromotive Force
20.1.1 Sources of Electrical Energy
1. Different Forms of Energy
Energy can exist in various forms: mechanical, chemical, thermal, electromagnetic, light, and nuclear. Any one of these forms of energy can be transformed into another. For example, mechanical energy, chemical energy, light energy, and thermal energy can be transformed into electrical energy.
2. Sources of Electrical Energy
Any device which can convert non-electrical energy into electrical energy is referred to as a source of electrical energy. For example, a battery is a source of electrical energy which contains chemicals. When these chemicals undergo chemical reactions, chemical energy is gradually depleted from the chemicals. The chemical energy that is lost reappears in the form of electrical energy. Other examples of sources of electrical energy are the dynamo (converting mechanical energy to electrical energy) and the photovoltaic cell (converting light energy to electrical energy).
20.1.2 Electromotive Force
1. Voltage at Terminals of Source of Electrical Energy
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| Figure 20.1. A battery with two terminals, X and Y, where energy is used to accumulate negative charges at terminal X, making it negatively charged, and to remove negative charges from terminal Y, making it positively charged. |
2. Electromotive Force
A voltage always exists across the terminals X and Y of a working source of electrical energy, irrespective of whether the source is connected to an external circuit or not, i.e., irrespective of whether there is any current flowing through the source of electrical energy or not. If no current flows through the source of electrical energy, the voltage that exists across X and Y is known as the electromotive force (emf) of the source.
One way to define emf is to use the equation:
work $W_s$ done in transferring positive charge q from X (-) to Y (+) though the source = (charge q) $\times$ (emf E)
or,
$E = \frac{W_s}{q}$
Hence, the emf of a source of electrical energy is the amount of (non-electrical) energy that needs to be expended by the source in order to transfer one coulomb of positive charge from the negative terminal to the positive terminal through the source.
(Note: Emf is also defined as the line integral of the non-conservative electric field found within the source of electrical energy.)
20.1.3 Potential Difference
1. Electric Pressure Difference
Suppose a positively charged particle is found at region A inside an electrical load such as an ohmic conductor (may even be in free space), as shown in Figure 20.2(a). It will not move towards another region B, which is some distance away since there is no net electric force acting on it.
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| Figure 20.2 Suppose a positively charged particle is found at region A inside an electrical load such as an ohmic conductor (may even be in free space), as shown in Figure 20.2(a). It will not move towards another region B, which is some distance away since there is no net electric force acting on it. Suppose we make part A of the ohmic conductor positively charged and B negatively charged. In this case, the positively charged particle will drift towards B because it is now acted on by a net electric force, as shown in Figure 20.2(b). We may imagine that there exists an “electric pressure difference” between A and B. This pressure difference causes charged particles to flow, thus producing an electric current in the conducting material. |
Suppose we make part A of the ohmic conductor positively charged and B negatively charged. In this case, the positively charged particle will drift towards B because it is now acted on by a net electric force, as shown in Figure 20.2(b). We may imagine that there exists an “electric pressure difference” between A and B. This pressure difference causes charged particles to flow, thus producing an electric current in the conducting material.
This is analogous to the hydrostatic pressure difference that exists across the two ends of a tube filled with liquid. This liquid pressure difference will cause the liquid to flow in the tube.
2. Electric Potential Difference
(a) The ‘electric pressure difference’ can be felt by the charged particles whenever a difference in electric potential exists across A and B. In other words, the ‘electric pressure difference’ is produced by the electric potential difference (p.d.) across A and B.
(b) Work is done by the electric force in pushing positive charges from A to B through the load. The amount of work done by the electric force is a measure of the electric potential difference across AB. We define the electric p.d. as follows:
The electric potential difference across points A and B is the amount of work done in moving unit charge from A to B.
3. Unit
The unit of electric potential difference is J C-1 or volt (V).
4. Defining Equation
Suppose the amount of work done in moving q coulomb of charge at point A to another point B is W joule. Then, by definition, the electric potential difference across A and B is given by:
$\Delta V_{AB}= \frac{W_L}{q}$
Normally, we drop the symbol Δ and the subscript AB and write:
$ V=\frac{W_L}{q}$
5. Definition of One Volt
Let $W_L = 1 \ J$ and $q = 1 \ C$. Then $\Delta V = 1 \ V$. Hence, an electric potential difference of one volt exists across two points when the amount of work done in moving one coulomb of charge from one point to another is one joule.
20.1.4 Heat Dissipation by Ohmic Conductor
1. Conversion of Energy
Refer to Figure 20.2(b). A positively charged particle at A is at higher electric potential than a similar positively charged particle at B. Hence, the positively charged particle at A will try to accelerate towards B through the conductor.
Due to the non-stop interactions with the atoms of the conductor, the particle continuously loses electrical energy as it drifts towards B. The electrical energy lost is converted to thermal energy, which is dissipated by the conductor to the surroundings.
2. Power Dissipation in Ohmic Conductors
Thermal energy is dissipated by an ohmic conductor as electric current flows continuously through the conductor. We have
thermal energy dissipated per second by an ohmic conductor = electrical energy lost per second in conductor. This is also defined as the work done per second.
power dissipased by ohmic conductor = work done ($W_L$) per second in conductor
$P_{dissipated}=\frac{qV}{1 \ second} = \left(\frac{1}{1 \ s}\right)V$
$P_{dissipated}=VI$
where I is the current flowing through the conductor and V is the potential difference across it.
Hence, the power dissipated by an ohmic conductor is given by
$\boxed{P = VI}$
If the ohmic conductor has resistance R, then using Ohm’s Law:
$V = IR$
We can write:
$\boxed{P = I(IR) = I^2R}$
3. Amount of Heat Dissipated
The amount of heat Q dissipated by an ohmic conductor in time t second is given by:
$P_{dissipated} = \frac{Q}{t}$
Thus:
$Q = P_{dissipated}t$
Substituting $P = IV$:
$\boxed{Q = IVt}$
4. Total Power Dissipated
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| Figure 20.3. Two ohmic conductors connected in series to a source of electrical energy. The electrical energy supplied by the source is distributed across the conductors, where it is dissipated as heat due to resistance. |
Suppose we have two electrical loads in the form of ohmic conductors connected in series to a source of electrical energy, as shown in Figure 20.3. We may look at this setup from the energy point of view. We have
(a) the electrical energy source
The main purpose of the source of electrical energy is to generate and deliver electrical energy to all the electrical loads which are connected to the source.
(b) the external loads
The ohmic conductors receive the electrical energy and convert it to heat. The total power dissipated by all the ohmic conductors is equal to the electrical power generated by the electrical source, i.e.,
$P_{dissipated} = P_{generated}$
$P_{dissipated}=V_1I + V_2I$
where I is the current through each conductor, and $V_1$ and $V_2$ are the potential differences across each conductor.
Applications of Electromotive Force (EMF), Potential Difference, and Heat Dissipation
1. Electric Circuits in Daily Life
Electromotive force (EMF) is widely used in electrical devices such as batteries, generators, and power supplies. These devices provide the energy needed to move charges through a circuit, allowing electrical appliances like lights, fans, and televisions to operate.
2. Charging and Power Supply Systems
Potential difference plays an important role in charging systems such as mobile phone chargers and laptop adapters. A suitable voltage ensures that electrical energy is transferred safely and efficiently to the device.
3. Heating Devices
Heat dissipation is applied in devices such as electric heaters, kettles, and irons. In these devices, electrical energy is converted into heat energy using resistive elements. The heat produced can be calculated using:
$Q = IVt$
4. Electrical Safety Devices
Understanding heat dissipation is important in designing safety devices such as fuses and circuit breakers. These devices prevent overheating by cutting off the current when excessive heat is generated.
5. Electronic Components
In electronic circuits, resistors are used to control current and voltage. However, they also dissipate heat. Proper design ensures that components do not overheat and become damaged.
6. Power Transmission
In power transmission systems, electrical energy is transferred over long distances. Engineers reduce heat loss by increasing voltage and decreasing current, since power loss depends on:
$P = I^2R$
7. Renewable Energy Systems
EMF is also generated in renewable energy systems such as solar panels and wind turbines. These systems convert natural energy sources into electrical energy for household and industrial use.
Conclusion
Electromotive force (EMF), potential difference, and heat dissipation are essential concepts in understanding how electrical circuits function. EMF represents the energy supplied by a source to move charges through a circuit, while potential difference measures the work done per unit charge between two points.
When electric current flows through a conductor, part of the electrical energy is converted into thermal energy due to resistance. This process, known as heat dissipation, is described by the equation:
$Q = IVt$
These concepts are closely related and play a crucial role in the design and operation of electrical systems. From simple household devices to complex power transmission networks, understanding EMF, voltage, and heat dissipation helps improve efficiency, safety, and performance.
In conclusion, mastering these fundamental principles allows students and engineers to analyze electrical circuits effectively and apply them in real-world situations.
Frequently Asked Questions (FAQ)
1. What is Electromotive Force (EMF)?
Electromotive force (EMF) is the energy supplied by a source per unit charge to move electric charges through a circuit. It is measured in volts (V).
2. What is the difference between EMF and potential difference?
EMF refers to the total energy supplied by a source, while potential difference (voltage) is the energy used per unit charge between two points in a circuit.
3. What is the formula for potential difference?
The potential difference is given by:
$V = W/q$
4. What is heat dissipation in an electrical circuit?
Heat dissipation is the process by which electrical energy is converted into thermal energy when current flows through a conductor due to resistance.
5. What is the formula for heat produced?
The heat produced in a conductor is given by:
$Q = IVt$
6. Why does a conductor produce heat?
A conductor produces heat because moving electrons collide with atoms in the material, converting electrical energy into thermal energy.
7. What is the unit of EMF and potential difference?
Both EMF and potential difference are measured in volts (V), where 1 volt = 1 joule per coulomb.
8. What is power dissipation in a conductor?
Power dissipation is the rate at which electrical energy is converted into heat energy in a conductor. It is given by:
$P = IV$
9. What are alternative formulas for power?
Power can also be expressed as:
$P = I^2R$ or $P = V^2/R$
10. Where are these concepts used in real life?
These concepts are used in everyday electrical devices such as heaters, chargers, power supplies, and large-scale electrical systems like power transmission networks.
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