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Module 4: Electrons, waves, and photons›Internal resistance (4.3.2)

Internal resistance (4.3.2)

E.m.f., terminal potential difference, internal resistance, lost volts, ε = I(R + r), and power dissipation in cells in A-level Physics.

3 min

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The electromotive force (EMF) of a source in a circuit, such as a cell or battery, is the energy per unit charge transferred from chemical energy to electrical energy.

Internal resistance Real cells and batteries have some resistance to the flow of current within themselves. This resistance causes energy to be lost as heat inside the source.

Generally, the voltage across the terminals of a cell or battery is less than its EMF as some energy is lost due to internal resistance.

A diagram showing a circuit with a battery represented by ε, a resistor labeled r, and the terminals of the cell indicated at both ends.

A real cell of EMF, and internal resistance, can be modelled as an ideal cell (defined as a cell with no internal resistance) of EMF, in series with a fixed resistor of resistance

The electromotive force, (EMF) of a source in a circuit such as a cell or battery is energy per unit charge transferred from chemical energy to electrical energy. Note that some of this electrical energy will be dissipated as heat across the internal resistance.

The terminal potential difference, of a cell or battery is the energy per unit charge transferred to electrical energy in the external circuit. The terminal potential difference of a cell or battery can be measured by connecting a voltmeter across its terminals.

‘Lost volts’ refers to the energy per unit charge wasted as heat inside a battery or cell. It is the drop in potential across the battery or cell’s internal resistance.

Due to Kirchhoff’s second law (conservation of energy), we have:

A circuit diagram showing a battery with voltage +ε, a resistor labeled r with voltage -v, and another resistor labeled R with voltage -V.

It is important to recall the potential difference across the terminals of a battery or cell.

A diagram illustrating a circuit with a potential difference equation. It shows a battery with a positive terminal labeled +ε, a resistor labeled r, and a resistor labeled R. The potential difference is represented as ε - v, with arrows indicating the direction of current flow.

Do

Recall that the potential difference across the terminals of a battery or cell is less than its EMF due to an internal resistance (unless the question states that internal resistance is negligible).

A circuit diagram showing a potential difference represented by ε, with a positive ε indicated. The diagram includes a resistor labeled R.

Don't

Assume that the potential difference across the terminals of a battery or cell is equal to its EMF (unless the question states that internal resistance is negligible).

Question walkthrough

Explaining Why Terminal Voltage Is Less Than EMF

Explain why the terminal voltage of a cell in series with a resistor is less than its EMF, in terms of internal resistance and energy loss.

Question walkthrough

Calculating Lost Voltage Due to Internal Resistance

Calculate the lost voltage across a battery's internal resistance, given the EMF, external resistance, and current from the ammeter reading.

Lost volts, due to internal resistance inside a source of EMF is given by:

Where:

is the current flowing through the source of EMF, and
is its internal resistance.

Terminal potential difference, of a source of EMF is given by:

Where:

is the current flowing through the source of EMF, and
is the total resistance of the external circuit.

The EMF of a source is given by:

which may be written as:

+ε -v = -lr r R -V = -IR

To determine internal resistance and EMF of a power source:

Set up a circuit with a variable resistor connected in series with the power source.
Vary the resistance of the variable resistor and record voltage and current.
Plot a graph of against
The equation, tells us that the Y intercept gives the EMF and the gradient of the line gives the negative internal resistance

A circuit diagram on the left showing a battery labeled 'A', a resistor labeled 'r', and a voltmeter labeled 'V'. On the right, a graph with 'V' on the vertical axis and 'I' on the horizontal axis, showing a downward sloping line with the label 'Gradient = -r' and several 'x' marks along the line.

Question walkthrough

Calculating Lost Volts and Internal Resistance of a Battery

Calculate the lost volts and internal resistance of a battery in series with a resistor, given the EMF and circuit current.

Question walkthrough

Finding Internal Resistance from Voltmeter Percentage Drop

Determine the internal resistance of a cell in terms of the external resistance, given the percentage decrease in voltmeter reading when a switch is closed.

Question walkthrough

Finding EMF in Two Opposing Cells Circuit

Calculate the EMF of a cell using two cells with opposing EMFs and internal resistance connected to an external resistor, applying Kirchhoff's voltage law to a single-loop circuit.