🔋 Chapter 46: EMF and Potential Difference of a Cell (Class XII)
🔷 1. Introduction
Every electrical circuit requires a source of electrical energy to maintain the flow of electric current. This source may be a cell, battery, or generator. Two important quantities associated with every electrical source are Electromotive Force (EMF) and Potential Difference (PD).
Although both EMF and potential difference are measured in volts (V), they are not the same. EMF represents the total energy supplied by the source, whereas potential difference represents the energy actually delivered to the external circuit.
🔷 2. What is Electromotive Force (EMF)?
Ethan: Professor, what is Electromotive Force or EMF?
Professor: Electromotive Force (EMF) is the energy supplied by a cell to move a unit positive charge completely around an electrical circuit.
Academic Definition
Electromotive Force (EMF) is the work done by a source in moving a unit positive charge once around the complete electrical circuit.
The symbol for EMF is E or ε (epsilon).
🔷 3. Formula for EMF
Ethan: Professor, what is the mathematical expression for EMF?
Professor: EMF is defined as the work done per unit charge.
E = W/Q
where,
- E = Electromotive force (volt)
- W = Work done by the cell (joule)
- Q = Charge moved (coulomb)
🔷 4. What is Potential Difference?
Ethan: Professor, what is potential difference?
Professor: Potential difference is the amount of electrical energy converted or used when a unit positive charge moves between any two points of an electrical circuit.
Academic Definition
Potential difference between two points is the work done in moving a unit positive charge from one point to another.
🔷 5. Formula for Potential Difference
Ethan: Professor, what is the mathematical expression for potential difference?
Professor: It is also defined as work done per unit charge.
V = W/Q
where,
- V = Potential difference (volt)
- W = Work done (joule)
- Q = Charge (coulomb)
🔷 6. Difference Between EMF and Potential Difference
Ethan: Professor, both formulas look the same. What is the difference between them?
Professor: The mathematical form is the same, but the physical meanings are different.
| Electromotive Force (EMF) | Potential Difference (PD) |
|---|---|
| Energy supplied by the source. | Energy used by circuit elements. |
| Exists even when no current flows. | Usually measured when current flows. |
| Represents the maximum voltage of the cell. | Represents the terminal voltage of the cell. |
| Depends on the source. | Depends on the external circuit. |
| Always greater than or equal to terminal voltage. | Usually less than EMF when current flows. |
🔷 7. Internal Resistance of a Cell
Ethan: Professor, why is the terminal voltage usually less than the EMF?
Professor: Every practical cell has an internal resistance. When current flows, some energy is lost inside the cell itself. Therefore, the voltage available at the terminals becomes smaller than the EMF.
🔷 8. Relation Between EMF and Terminal Potential Difference
Ethan: Professor, what is the relation between EMF and terminal voltage?
Professor: If a cell of internal resistance r supplies current I, then the terminal potential difference is given by:
V = E − Ir
where,
- V = Terminal potential difference
- E = EMF of the cell
- I = Current flowing through the circuit
- r = Internal resistance of the cell
🔷 9. Open Circuit Condition
Ethan: Professor, what happens when no current is drawn from the cell?
Professor: When the circuit is open, no current flows.
I = 0
Substituting this into the terminal voltage equation,
V = E
Thus, under open-circuit conditions, the terminal voltage is equal to the EMF of the cell.
🔷 10. Short Circuit Condition
Ethan: Professor, what happens if the terminals of a cell are connected directly?
Professor: This is called a short circuit. The external resistance becomes nearly zero, causing a very large current to flow. Such a condition may damage the cell because excessive power is dissipated inside it.
🔷 11. Applications
- Design of batteries.
- Electrical power systems.
- Battery performance analysis.
- Electronic circuit design.
- Measurement of terminal voltage.
- Rechargeable battery technology.
📦 12. Important Results (Must Remember)
- EMF is the energy supplied per unit charge by the source.
- Potential difference is the energy used per unit charge between two points.
- Both are measured in volts.
- EMF exists even when no current flows.
- Terminal voltage decreases when current flows due to internal resistance.
- Terminal voltage equation: V = E − Ir.
- For an open circuit, V = E.
- EMF is always greater than or equal to the terminal potential difference during discharge.
🧠 13. Conceptual Questions
🔹 Q1
Ethan: What is EMF?
Professor: It is the work done by a source in moving a unit positive charge around the complete circuit.
🔹 Q2
Ethan: What is potential difference?
Professor: It is the work done per unit charge in moving a charge between two points in a circuit.
🔹 Q3
Ethan: Why is the terminal voltage less than the EMF when current flows?
Professor: Because part of the energy is lost inside the cell due to its internal resistance.
🔹 Q4
Ethan: Under what condition is the terminal voltage equal to the EMF?
Professor: When no current flows through the circuit (open circuit).
🔹 Q5
Ethan: What is the relation between EMF and terminal potential difference?
Professor: V = E − Ir.
🔷 14. Summary
Electromotive Force (EMF) is the total energy supplied by a cell per unit charge, while potential difference is the energy delivered or consumed per unit charge between two points in a circuit. Although both are measured in volts, EMF represents the maximum voltage of the cell, whereas the terminal potential difference decreases when current flows because of the cell's internal resistance. The relationship V = E − Ir explains how the terminal voltage depends on the current and the internal resistance of the cell.
✨ End of Topic: EMF and Potential Difference of a Cell ✨
0 Comments