🔋 1. What is an Electric Cell?
An electric cell is a device that converts chemical energy into
electrical energy and maintains a potential difference between its
terminals.
Positive Terminal
Higher electric potential.
Negative Terminal
Lower electric potential.
EMF
Energy supplied per unit charge by the cell.
Internal Resistance
Resistance offered inside the cell.
⚡ 2. Electromotive Force (EMF)
The electromotive force of a cell is the work done by the source in
moving unit positive charge around the complete circuit.
ε = W/q
The SI unit of EMF is volt (V).
⭐ EMF is not actually a force. It represents energy supplied per unit
charge by the source.
🔌 3. Internal Resistance of a Cell
A real cell contains electrolyte and electrodes that oppose the motion
of charge carriers. This opposition is called the internal resistance
of the cell.
Internal Resistance = r
When current flows through the cell, some potential difference is lost
inside the cell.
Internal Potential Drop = Ir
📐 4. Relation Between EMF and Terminal Potential Difference
Consider a cell of EMF ε and internal resistance r supplying current I
through an external resistance R.
The potential drop inside the cell is:
Ir
Therefore terminal potential difference is:
V = ε − Ir
Hence:
ε = V + Ir
This is the fundamental relation for a discharging cell.
🔋 5. Terminal Potential Difference
The potential difference measured across the terminals of a cell while
it is supplying current is called terminal potential difference.
V = ε − Ir
Therefore, during discharge:
I ↑ → Ir ↑ → V ↓
⭐ Terminal voltage is less than EMF when a cell supplies current.
🔌 6. Open Circuit Condition
When the external circuit is open, no current flows through the cell.
Therefore:
I = 0
Using:
V = ε − Ir
we get:
V = ε
Therefore, the terminal potential difference of an ideal open-circuit
cell is equal to its EMF.
🔬 7. Interactive Cell Practical
EMF ε
Conventional Current →
R
EMF:
6.00 V
Internal Resistance:
2.00 Ω
External Resistance:
10.00 Ω
Current:
0.50 A
Terminal Voltage:
5.00 V
Internal Voltage Drop:
1.00 V
Relation:
ε = V + Ir
🧮 8. Derivation of Current in a Circuit
The cell of EMF ε and internal resistance r is connected to an external
resistance R.
Total resistance of the circuit:
Rtotal = R + r
According to Ohm's law:
I = ε/(R+r)
Therefore:
I = ε/(R+r)
📊 9. Terminal Voltage in Terms of External Resistance
We know:
V = IR
and:
I = ε/(R+r)
Therefore:
V = εR/(R+r)
Hence:
V = εR/(R+r)
📈 10. Charging and Discharging of a Cell
🔴 Discharging
Cell supplies current to the external circuit.
V = ε − Ir
Terminal voltage is less than EMF.
🟢 Charging
An external source forces current into the cell.
V = ε + Ir
The applied terminal voltage is greater than the EMF.
⚙️ 11. Factors Affecting Internal Resistance
Electrolyte
Higher concentration generally changes ionic conductivity and therefore
internal resistance.
Distance Between Electrodes
Greater separation generally increases internal resistance.
Area of Electrodes
Larger effective electrode area generally decreases internal resistance.
Temperature
For many cells, increasing temperature increases ionic mobility and can
reduce internal resistance.
🔗 12. EMF vs Terminal Potential Difference
EMF (ε)
- Energy supplied per unit charge.
- Measured under open-circuit condition.
- Represents maximum potential difference of a cell.
- Unit: volt.
Terminal Voltage (V)
- Potential difference across terminals while operating.
- Depends on current.
- During discharge V < ε.
- Unit: volt.
🧪 13. Solved Numerical
Question:
A cell has EMF 12 V and internal resistance 2 Ω. It is connected to an
external resistance of 10 Ω. Find the current and terminal voltage.
I = ε/(R+r)
I = 12/(10+2)
I = 1 A
Terminal voltage:
V = IR
V = 1 × 10
Terminal Voltage = 10 V
Internal voltage drop:
Ir = 1 × 2 = 2 V
Check:
ε = V + Ir = 10 + 2 = 12 V
📝 14. MCQ Practice
1. EMF of a cell is defined as:
A. Charge per unit energy
B. Energy supplied per unit charge
C. Current per unit resistance
D. Resistance per unit current
✔ Answer: B
2. SI unit of EMF is:
A. Ampere
B. Ohm
C. Volt
D. Coulomb
✔ Answer: C
3. Terminal voltage of a discharging cell is:
A. ε + Ir
B. ε − Ir
C. Ir − ε
D. εIr
✔ Answer: B
4. Current supplied by a cell is:
A. εR/r
B. ε/(R+r)
C. ε(R+r)
D. R/(ε+r)
✔ Answer: B
5. If no current is drawn from a cell, terminal voltage is:
A. Zero
B. Less than EMF
C. Equal to EMF
D. Greater than EMF
✔ Answer: C
6. Internal voltage drop in a cell is:
A. IR
B. Ir
C. εR
D. ε/r
✔ Answer: B
7. When a cell is being charged, terminal voltage is:
A. ε − Ir
B. ε + Ir
C. ε only
D. Zero
✔ Answer: B
8. Internal resistance of a cell is represented by:
A. R
B. r
C. V
D. I
✔ Answer: B
9. If external resistance increases, current supplied by the cell:
A. Increases
B. Decreases
C. Remains constant
D. Becomes infinite
✔ Answer: B
10. Maximum current from a cell is obtained when:
A. R = ∞
B. R = r
C. R = 0
D. R > r
✔ Answer: C
🟢 15. 2 Marks — 6 Questions
Q1
Define EMF of a cell and write its SI unit.
Q2
Define internal resistance of a cell.
Q3
Define terminal potential difference.
Q4
Write the relation between EMF and terminal voltage of a discharging cell.
Q5
What is the terminal voltage of a cell when no current is drawn from it?
Q6
Write the expression for current supplied by a cell having internal resistance.
🟡 16. 3 Marks — 6 Questions
Q1
Derive ε = V + Ir for a discharging cell.
Q2
Derive I = ε/(R+r).
Q3
Differentiate between EMF and terminal potential difference.
Q4
Explain why terminal voltage is less than EMF when a cell supplies current.
Q5
What happens to terminal voltage when the current drawn from a cell increases?
Q6
Explain the significance of internal resistance of a cell.
🟠 17. 4 Marks — 6 Questions
Q1
Derive the relation between EMF, terminal voltage, current and internal resistance.
Q2
Derive the expression for current in a circuit containing a cell of internal resistance.
Q3
Explain open-circuit and closed-circuit conditions of a cell.
Q4
Explain the factors affecting the internal resistance of a cell.
Q5
Differentiate between EMF and terminal potential difference with suitable equations.
Q6
Derive V = εR/(R+r).
🔴 18. 5 Marks — 6 Questions
Q1
Explain EMF and terminal potential difference and derive their relation for a discharging cell.
Q2
Derive the expression I = ε/(R+r) and explain the role of internal resistance.
Q3
Explain how internal resistance affects the terminal voltage of a cell.
Q4
Derive the expression for terminal potential difference in terms of EMF, external resistance and internal resistance.
Q5
Discuss the factors affecting internal resistance of an electrochemical cell.
Q6
Explain the difference between a cell's EMF and terminal voltage during charging and discharging.
🔵 19. 6 Marks — 6 Questions
Q1
Derive the relation ε = V + Ir for a cell supplying current and explain each term.
Q2
Derive the current I = ε/(R+r) and terminal potential difference V = εR/(R+r).
Q3
Explain in detail the concept of EMF, internal resistance and terminal potential difference.
Q4
A cell of EMF ε and internal resistance r is connected to an external resistance R. Derive all important expressions for current and terminal voltage.
Q5
Explain experimentally how EMF and internal resistance of a cell can be determined.
Q6
Discuss the behaviour of a practical cell under open circuit, discharge and charging conditions with suitable equations.
🔬 20. Practical: Determination of EMF and Internal Resistance
Apparatus
Cell, resistance box, rheostat, ammeter, voltmeter, key and connecting
wires.
Principle
V = ε − Ir
Comparing with the straight-line equation:
y = c + mx
we can write:
V = ε − rI
Thus, a graph of
V versus I is a straight line.
- Y-intercept = ε
- Slope = −r
Therefore:
r = −Slope
🚀 Quick Revision
EMF:
ε = W/q
Internal Voltage Drop:
Ir
Discharging Cell:
V = ε − Ir
Charging Cell:
V = ε + Ir
Current:
I = ε/(R+r)
Terminal Voltage:
V = IR
Terminal Voltage in Terms of R:
V = εR/(R+r)
Open Circuit:
I = 0 ⇒ V = ε
Important Relation:
ε = V + Ir
