EMF and Internal Resistance

Complete Electrical Circuits

What is internal resistance?

The resistance inside a source of emf, such as a cell or battery.

What symbol is used for internal resistance?

r

What is the unit of internal resistance?

Ohms (Ω).

What causes internal resistance?

The materials inside a cell resist the movement of charge, causing some energy to be transferred as heat.

How can a real cell be modelled?

As a source of pure emf, ε, connected in series with an internal resistance, r.

Why is the internal resistance of an emf source often ignored?

It is usually small and may have little effect when the current is small.

What happens when a large current flows through a cell with internal resistance?

More energy is dissipated as heat inside the cell and the terminal potential difference decreases.

Why can a large current damage a cell?

Large currents cause significant heating due to the cell's internal resistance.

What are lost volts?

The potential difference across the internal resistance of a source.

What equation gives the lost volts?

Vlost = Ir

What does I represent in Vlost = Ir?

The current through the cell.

What does r represent in Vlost = Ir?

The internal resistance of the cell.

What is terminal potential difference?

The potential difference measured across the terminals of a cell when it is supplying current.

What equation links terminal pd, emf, current and internal resistance?

V = ε − Ir

What does ε represent in V = ε − Ir?

The emf of the source.

What does Ir represent in V = ε − Ir?

The lost volts across the internal resistance.

Why is terminal pd normally less than the emf when a cell supplies current?

Some energy per unit charge is transferred inside the cell due to its internal resistance.

Write the emf equation in terms of terminal pd and lost volts.

ε = V + Ir

How does the equation ε = V + Ir demonstrate conservation of energy?

The energy supplied per unit charge by the cell equals the energy transferred to the external circuit plus the energy transferred inside the cell.

What is the relationship between the terminal pd and the pd across the load resistance?

They are equal: Vterminal = Vload.

What happens to lost volts when current increases?

Lost volts increase because Vlost = Ir.

What happens to terminal pd when current increases?

It decreases because V = ε − Ir.

What happens to terminal pd when current decreases?

It increases towards the emf.

What is the terminal pd when no current flows through an ideal voltmeter?

It equals the emf because Ir = 0.

Why can the emf of a cell be measured when no current is drawn from it?

With I = 0, there are no lost volts, so V = ε.

What is the difference between emf and terminal pd?

Emf is the total energy supplied per unit charge by the source, while terminal pd is the energy per unit charge available to the external circuit.

How can internal resistance be calculated if ε, V and I are known?

r = (ε − V)/I.

A 6.0 V battery supplies 5.8 V at a current of 0.40 A. Calculate its internal resistance.

r = (6.0 − 5.8)/0.40 = 0.50 Ω.

A 1.5 V cell supplies a terminal pd of 1.3 V. What are the lost volts?

1.5 − 1.3 = 0.20 V.

A 1.5 V cell supplies 1.3 V to a 5.0 Ω lamp. Calculate the current.

I = V/R = 1.3/5.0 = 0.26 A.

A 1.5 V cell supplies 1.3 V to a 5.0 Ω lamp. Calculate its internal resistance.

r = (1.5 − 1.3)/0.26 ≈ 0.77 Ω.

Why should a car battery have a very low internal resistance?

The starter motor requires a very large current, so a low internal resistance reduces lost volts and energy wasted as heat.

Why can a car's headlights dim when the starter motor is used?

The starter motor draws a large current, increasing Ir and reducing the terminal pd supplied to the headlights.

How can internal resistance be investigated experimentally?

Connect a variable resistor and ammeter in series with the cell and a voltmeter across the cell, then vary the resistance and record I and V.

Why is a variable resistor used in an internal resistance experiment?

To change the current drawn from the cell.

What measurements are taken when investigating internal resistance?

Current I and terminal potential difference V.

What equation is used to analyse an internal resistance experiment?

V = ε − Ir.

How can V = ε − Ir be written in straight-line form?

V = −rI + ε.

What should be plotted on the y-axis when determining internal resistance graphically?

Terminal potential difference, V.

What should be plotted on the x-axis when determining internal resistance graphically?

Current, I.

What is the gradient of a graph of V against I?

−r.

How can internal resistance be found from a V against I graph?

Calculate the magnitude of the gradient: r = −gradient.

Why is the V against I graph expected to have a negative gradient?

As current increases, the lost volts Ir increase, so terminal pd decreases.

What does the y-intercept of a V against I graph represent?

The emf, ε.

Why does the y-intercept give the emf?

At I = 0, there are no lost volts, so V = ε.

What are the units of the gradient of a V against I graph?

V A⁻¹, which is equivalent to Ω.

How can emf be determined from an internal resistance experiment?

Find the y-intercept of the V against I graph.

How can internal resistance be determined from an internal resistance experiment?

Find the magnitude of the negative gradient of the V against I graph.

What happens to the terminal pd as the external resistance is reduced?

The current increases, causing greater lost volts, so terminal pd decreases.

What happens to the terminal pd as the external resistance is increased?

The current decreases, reducing lost volts, so terminal pd increases towards the emf.

Why does a voltmeter connected across a working cell not normally measure its emf?

When current flows, some pd is lost across the internal resistance, so the voltmeter measures ε − Ir.

What is the total resistance of a circuit containing an external resistance R and internal resistance r in series?

Rtotal = R + r.

Write an equation for current in terms of emf, external resistance and internal resistance.

I = ε/(R + r).

If internal resistance increases while emf and external resistance stay constant, what happens to current?

The current decreases.

If internal resistance increases, what happens to the proportion of energy wasted inside the cell?

It increases.

Why is a low internal resistance desirable in a power source?

It reduces energy loss and allows a larger terminal voltage and current to be supplied to the external circuit.

What happens to the energy associated with the lost volts?

It is mainly transferred to thermal energy inside the source.

State the key equation for internal resistance questions.

ε = V + Ir.

State the alternative form of the internal resistance equation.

V = ε − Ir.

State the graph equation used for internal resistance experiments.

V = −rI + ε.