Electric Cells (DP IB Physics: HL)

The diagram below shows two circuits A and B that were used by a student to test a battery of four identical cells. In circuit A, there was no load resistor and in circuit B a load resistor was connected. Assume that the meters in the circuits are ideal.

Explain why there is a difference in voltages recorded in the two circuits.

Calculate the internal resistance of a single cell.

In circuit B, the resistance of the load resistor R is altered so that a series of values on the voltmeter and the corresponding values of the current on the ammeter are obtained.

A cell is connected to an external resistor and the terminal voltage across the cell monitored. The graph shows the discharge time for one cell with a current of 0.5 A.

Determine the terminal voltage of the single cell. Show your working clearly.

The diagram shows a battery of e.m.f. 40.0 V and internal resistance, r.

The current in the battery is 2.5 A. 

Calculate the internal resistance r.

Calculate the energy dissipated in the battery in 3.5 minutes.

The circuit is amended to include a primary and a secondary cell. 

Explain the function of primary and secondary cells and the role they have in an electric circuit.

The internal resistance of the battery affects the efficiency of the transfer of energy from the battery to the circuit. 

Explain what causes internal resistance and why this affects the efficiency of the battery.

The diagram shows a cell of e.m.f. ε, and internal resistance, r, is connected to a variable resistor R. The current through the cell and the terminal p.d. of the cell are measured as R is decreased.

 The graph below shows the results from the experiment.

State the relationship between the terminal p.d. and current and explain why this relationship occurs.

Find the e.m.f., ε, and the internal resistance, r, of the cell.

Draw a line on the graph above to show the results obtained from a cell with the half the e.m.f. but double the internal resistance of the first cell. Label your graph A.

Draw a line on the same graph to show the results obtained from a cell with the same e.m.f. but negligible internal resistance. Label your graph B.

A battery is connected to an 9.0 Ω resistor. The e.m.f. of the battery is 12 V.

When the switch is open the voltmeter reads 12 V and when it is closed it reads 11.3 V. 

Explain why the readings are different.

Calculate the internal resistance of the battery.

The circuit diagram shows that the 9.0 Ω resistor is now connected in parallel with an unknown resistor, R. The battery now supplies a current of 3.0 A and has the same internal resistance r as the previous circuit.

Calculate the p.d. across the 9.0 Ω resistor.

Calculate the resistance of R.

A very high resistance voltmeter reads 11.5 V when it is connected across the terminals of a power supply. 

Explain why the reading on the voltmeter is equal to the E.m.f. of the power supply.

Calculate the potential difference between points X and Y in the circuit.

Calculate the internal resistance of the battery.

Explain the direction of the current flow required to recharge the secondary cell from the primary cell inside this circuit.

A uniform wire of length 80 cm and radius 0.50 mm is connected in series with a cell of e.m.f. 3.0 V and an internal resistance of 0.70 Ω.

The resistivity of the metal used to make the wire is 1.10 × 10^–6 Ω m. 

Determine the current that flows in the cell.  

A voltmeter is connected at X, with a movable probe C, such that the voltmeter is able to read the potential difference across the wire at different points between X and Y.

Sketch a graph on the set of axes below which shows how the potential difference V varies between X and Y as the sliding contact C moves from X to Y. 

The voltmeter in (b) is replaced with a cell of e.m.f. 1.5 V with internal resistance 0.50 Ω, and an ammeter:

The moveable contact can again be connected to any point along the wire XY. At point D, there is zero current in the ammeter. 

Calculate the length of XD. 

The Maximum Power Transfer theorem says the maximum amount of electrical power is dissipated in a load resistance R_L when it is exactly equal to the internal resistance of the power source r. 

The circuit below is used to investigate maximum power transfer.

A variable resistor, which acts as the load resistance R_L, is connected to a power source of e.m.f. and internal resistance r, along with a switch S and an ammeter and voltmeter.

The graph below shows the results obtained for the power P dissipated in R_L as the potential difference V across R_L is varied: 

Assuming the Maximum Power Theorem is valid, use the graph to determine the internal resistance of the power source. 

Show that the e.m.f. of the power supply is 9 V. 

Identify what happens to each of the following quantities as the value of the load resistance R_L becomes infinitely large: 

It can be shown that the power P dissipated in the load resistance R_L is zero when the load resistance is zero. 

Sketch a graph on the axes provided to show how the power dissipated P varies with load resistance R_L.  

Label the position of the internal resistance, r. 

The diagram shows a circuit which can be used to investigate the internal resistance r of a power supply. In this case, a battery consisting of six dry cells in series, each of e.m.f. ε = 0.5 V, is connected to an oscilloscope:

The chart below represents the trace shown on the oscilloscope screen when both of the switches S₁ and S₂ are open: 

The y-gain of the oscilloscope is set at 1.5 V div^–1. 

Discuss what happens to the trace shown on the oscilloscope screen when switch S₁ is closed.   

Draw the trace on the oscilloscope screen when both switches S₁ and S₂ are closed. Explain your answer.

Calculate the internal resistance of the battery if the vertical distance between the traces in part (a) and part (b) is measured to be half a division. 

Determine the current in the cell that would move the trace shown on the oscilloscope screen back to its original position as shown in part a. Assume both switches, S₁ and S₂, remain closed. 

Understanding the properties of e.m.f. and internal resistance can help the design decisions of architects and electrical engineers. 

In an experiment to investigate power dissipation across two lamps, L₁ and L₂, an engineer connects them in a series circuit to a cell of e.m.f. 45 V and internal resistance 7 Ω. 

The lamp L₁ has a resistance of 10 Ω and L₂ has a resistance of 25 Ω. 

Calculate the percentage difference between the power generated by the cell and the power dissipated in the two lamps L₁ and L₂. Suggest a reason for this percentage difference. 

The engineer wishes to maximise the power dissipated across each lamp and explores various alternatives to the circuit shown in part a.

Suggest and explain, using appropriate calculations, how the engineer should arrange the lamps L₁ and L₂ such that the power dissipated in each lamp is maximised. 

The engineer comes up with a theoretical problem, which involves arranging a large number of identical lamps in parallel with each other, as illustrated below:

The lamps are connected to a cell of e.m.f. ε and internal resistance r. 

Discuss the effect on the terminal p.d. supplied by the cell, and hence on the lamps, as more lamps are added in parallel.