EMF, Internal Resistance and Terminal Voltage
EMF of a cell is the work done by the source per unit charge in driving charge around the complete circuit. Internal resistance is the opposition to current within the cell, and terminal voltage is the potential difference available across the cell terminals when current flows.
In one line: A real cell keeps some voltage inside when it supplies current.
Concept Practice Coming SoonUnderstand it
- A real cell is not an ideal source.
- It has internal resistance r, so some energy per unit charge is lost inside the cell when current flows.
- During discharge, terminal voltage V is less than emf ε and is given by V = ε - Ir.
- During charging, terminal voltage can exceed emf because the external source pushes current into the cell.
- This distinction is important in practical circuits and numerical problems involving cells.
Example
Formula and rule
For a discharging cell: V = ε - Ir.
For a charging cell: V = ε + Ir.
Here V is terminal voltage in volt, ε is emf in volt, I is current in ampere, and r is internal resistance in ohm.
For identical cells in series, emf adds and internal resistance adds.
Conditions: use correct current direction and cell polarity.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
A cell has ε = 12 V and r = 1.0 ohm.
- 1It supplies current to an external resistance R = 5.0 ohm.
- 2Total resistance = R + r = 6.0 ohm, so I = ε/(R + r) = 12/6 = 2.0 A.
- 3Terminal voltage V = ε - Ir = 12 - 2 × 1 = 10 V.
- 4The external resistor receives 10 V, not the full emf.
Method you can reuse
- 1Represent the real cell as ε in series with r.
- 2Decide whether the cell is delivering or receiving current.
- 3Find total circuit resistance if an external resistor is given.
- 4Calculate current.
- 5Apply V = ε - Ir for discharge or V = ε + Ir for charging.
- 6Include volt and ohm units.
Sketch it in your answer
Draw a real cell as an ideal emf ε in series with internal resistance r, connected to an external resistance R. Label current direction, terminal points, terminal voltage V, and internal drop Ir.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why is the terminal voltage of a discharging cell less than its emf?
Think first, then show answerHide answer
Common wrong answer
Using V = ε + Ir for a discharging cell gives a terminal voltage greater than the emf, which contradicts energy loss inside the cell.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
EMF of a cell is the work done by the source per unit charge in driving charge around the complete circuit. Internal resistance is the opposition to current within the cell, and terminal voltage is the potential difference available across the cell terminals when current flows.
- 2
Add for 2 marks
Example: If a cell of emf 2.0 V and internal resistance 0.5 ohm supplies 1.0 A, its terminal voltage is 2.0 - 0.5 = 1.5 V.
- 3
Add for 3 marks
A real cell is not an ideal source.
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