Electrical power sources such as dry cells, accumulators, dynamos, and generators do work to drive electric charges around a complete circuit. However, real chemical cells are not ideal voltage sources; their own chemical electrolytes present an internal resistance that causes a drop in potential difference when current flows. Understanding the difference between electromotive force (\(\mathcal{E}\)) and terminal potential difference (\(V\)), as well as how cells behave in series and parallel arrangements, is crucial for designing efficient electrical systems ranging from basic household electronics to modern electric vehicles.
See how the vertical intercept gives the electromotive force (\(\mathcal{E}\)) and the magnitude of the negative gradient gives the internal resistance (\(r\)).
Understand e.m.f., internal resistance, and how they affect a real circuit.
Electromotive force is the energy transferred or work done by an electrical source to move one coulomb of charge in a complete circuit.
\(\mathcal{E} = \dfrac{E}{Q}\)
S.I. unit: volt (\(\text{V}\)) or joule per coulomb (\(\text{J C}^{-1}\)).
Internal resistance is the resistance caused by the electrolyte inside the dry cell. Its S.I. unit is ohm (\(\Omega\)).
It causes loss of energy as heat inside the cell and makes the terminal potential difference \(V\) less than the e.m.f. \(\mathcal{E}\) when current flows.
Fundamental relationship
where \(\mathcal{E}\) = e.m.f., \(V = IR\) = terminal potential difference, \(I\) = current, \(r\) = internal resistance, and \(R\) = external resistance.
For \(n\) identical cells with e.m.f. \(\mathcal{E}\) and internal resistance \(r\):
\(\text{Total e.m.f.} = n\mathcal{E}\)
\(r_e = nr\)
Increases total e.m.f., supplying higher voltage and delivering a larger current when the external resistance \(R\) is significantly large.
\(\text{Total e.m.f.} = \mathcal{E}\)
\(\dfrac{1}{r_e} = \dfrac{n}{r} \implies r_e = \dfrac{r}{n}\)
Decreases effective internal resistance, allowing the circuit to maintain a stable voltage and sustain current over longer usage.
Alkaline cells (using potassium hydroxide electrolyte) are twice as durable as zinc-carbon cells (using ammonium chloride electrolyte) and typically exhibit lower internal resistance.
Electric vehicles (E.V.) are 100% electrically powered via rechargeable batteries (e.g., Li-Ion or Ni-MH) powering electric motors. Operating battery voltage range: \(300\text{ – }800\text{ V}\).
Hybrid cars use \(25\text{ – }40\%\) of power supplied by rechargeable batteries (operating range \(100\text{ – }200\text{ V}\)), with the remainder provided by fossil fuels (petrol).
Solar panels: solar cells are connected in series to step up voltage and combined in parallel to supply sufficient operating current.
Answer in your mind, then press “Check Answer”.
What is meant by the electromotive force (e.m.f.) of a cell?
Why is the reading of a voltmeter connected across the terminals of a dry cell lower in a closed circuit compared to an open circuit?
Two identical dry cells, each with an e.m.f. of \(1.5\text{ V}\) and an internal resistance of \(0.5\ \Omega\), are connected in parallel to an external resistor of \(10\ \Omega\). What is the total current flowing in the circuit?
Electromotive force is a physical mechanical force measured in Newtons.
Despite the word “force”, e.m.f. is not a mechanical force. It is an electrical energy quantity per unit charge, measured in volts (\(\text{V}\)) or joules per coulomb (\(\text{J C}^{-1}\)).
Internal resistance is an external resistor added to protect the cell.
Internal resistance is an inherent physical property inside the cell itself, caused by the resistance of its chemical electrolyte and electrode materials to the flow of charges.
The potential difference across the terminals of a cell is always equal to its e.m.f.
The terminal potential difference equals the e.m.f. only when the circuit is open (current \(I = 0\)). In any closed circuit drawing current, \(V\) is always less than \(\mathcal{E}\) due to the internal voltage drop \(Ir\).
Objective: Test your understanding of e.m.f., internal resistance, and cell arrangements.
1 Which statement correctly explains why the terminal potential difference across a dry cell decreases when the switch in a circuit is closed?
2 In an experiment to determine the e.m.f. and internal resistance of a dry cell, a student plots a graph of terminal potential difference (\(V\)) against current (\(I\)). How are the e.m.f. (\(\mathcal{E}\)) and internal resistance (\(r\)) determined from the graph?
3 The resistance caused by the electrolyte inside a dry cell is known as .
4 Connecting multiple identical dry cells in parallel does not change the total e.m.f., but it reduces the effective of the cells.
Drag each term to the correct description. If using a phone, tap the answer first, then tap the matching box.
There is something wrong with this question.
