Current & Circuits (HL IB Physics)

In a circuit, a current of 2.0 A flows through a resistor for 90 minutes.

Determine the number of electrons that pass a point in the resistor this time.

The current in (a) flows across a potential difference of 12 V.

Using your answer to (a), calculate the total energy transferred in the circuit.

When a copper wire is exposed to a potential difference, a current is detected in it.

Explain, with reference to charge carriers, why there is a current detected in the wire.

A student is investigating the electrical resistivity of a thin film of carbon.

Calculate the current which passes through the carbon film when a potential difference of 2.5 mV is applied across it.

The resistivity of carbon is 4.0 × 10^–5 Ω m.

A current I = 10 A flows through a network of six resistors as shown.

The potential difference across the line XY is 8 V.

Calculate the value of the unknown resistance R.

Another network, comprised of four identical resistors each of resistance 2 Ω, is connected to a 6 V battery with negligible internal resistance.

Determine the reading on the ammeter.

A resistor is made by connecting two uniform cylinders X and Y of the same material and equal in length, in series.

Cylinder Y has a resistance of 5 Ω and is twice the diameter of cylinder X.

Calculate the total resistance of this series combination.

State and explain why knowledge of quantities like resistivity is useful to scientists.

A variable resistor R₁ has a resistance that varies between 0 and 10 Ω is connected to two resistors R₂ and R₃ and two cells of e.m.f. 5 V and 6 V.

Deduce an expression for three currents I₁, I₂ and I₃ at the junction between the resistors R₁, R₂ and R₃.   

Initially, the variable resistor  is set to 0 Ω.

If R₂ is 5 Ω and R₃ is 10 Ω, determine the current through resistor R₂.

A circuit includes three fixed resistors and a thermistor with variable resistance R.

The battery has an e.m.f. of 12 V, with negligible internal resistance. At room temperature, the resistance of the thermistor is 4.0 kΩ.

Calculate the current in the battery at room temperature.

An electronic circuit contains two resistors connected as shown.

The material from which each resistor is made has a resistivity of 2.0 × 10⁵ Ω m and both resistors have dimensions of 15 mm by 2.3 mm by 1.3 mm.

Calculate the total resistance of the electronic circuit.

The circuit is designed such that changes to the dimensions of each resistor by a common factor  are easily accomplished.

Show that if the dimensions of each resistor are increased by a factor of  then the resistance decreases by the same factor.

An electrical heating element is made of nichrome wire of resistivity 1.1 × 10^–6 Ω m. It is required to dissipate 800 W when connected to the 230 V mains supply. The radius of the wire is 0.17 mm.

Calculate the length of wire required for the heating element.

Suggest two properties that the nichrome wire must have to make it suitable as an electrical heating element.

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.

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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 solar cell. 

Explain the function of a solar cell and an advantage it has in an electric circuit over a chemical cell.

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

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

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.

A combination of identical resistors each with resistance R has a total resistance of 250 Ω. 

Show, without the use of a calculator, how to find the value of resistance of each resistor and hence determine the value of R.

A student is provided with four fixed resistors of the following sizes:

1 × 5.0 Ω

1 × 10.0 Ω

2 × 20.0 Ω

Calculate the maximum power which can be drawn from a circuit which uses all four resistors connected to a variable power supply with terminal voltage ranging from 2-12 V. Include a sketch of the circuit you have outlined in your answer.

A physics class planned an investigation into electromotive force (emf) and internal resistance. When the students arrived the equipment had not been set out as they expected. They were provided with the circuit diagram shown, and a set of ten fixed resistors, ranging from 10-200 Ω in regular increments which could be used in place of the resistor, R.

Comment on how the students can use their results to find both the emf and the internal resistance of the cell and hence suggest the outcome of this investigation.  

Assume that the ammeter is suitable to measure all the currents which this circuit may produce. No additional equipment may be used.

The circuit diagram shows a battery which has negligible internal resistance connected to three resistors which have different values of resistance.

A current of 2.0 mA flows in an ammeter for 90 minutes. 

Calculate the approximate number of electrons which pass through the ammeter in this time.

Human skin tissue has much higher resistivity than muscle tissue. Typical values for the resistivity of particular tissue types vary. For this question use the data in the table below.

A person grasps a wire which has a diameter of 0.5 cm at a potential of 12 V. The wire is not insulated and the person is well earthed. The skin of the hand is 1.0 mm thick and is in contact with the whole wire for a distance of 10 cm.

Following the accident in part (b) the teacher sets a research homework, where students are asked to discuss electrical safety. 

By comparing the factors given in the question

High voltage electrical accidents can cause deep burns throughout the body, which often require major surgery and can lead to permanent disability or death.

Outline the reasons for this level of injury, stating two assumptions that you have made in your explanation.

The variation with temperature of the resistance, R_T of a thermistor with temperature is shown.

The thermistor is connected into a circuit using a power source with negligible internal resistance. The temperature is 22.5 °C.

Show, without the use of a calculator, how to determine the reading on the voltmeter, giving the answer to two significant figures.

The temperature is changed so that the voltmeter reads 4.0 V. 

Determine the new temperature.

Show that and hence express the unit represented by these equations in S.I. units.

A family on a tight budget needs to buy a new electric heater. The retailer's website, written (it claims) by electrical engineers, suggests that the best value-for-money heater has very high resistance because .

The family, who all study physics, think that a low resistance heater would be better, because .

Explain who is correct.

Two thin strips of silver and of iron have the same dimensions. The strips are connected to a circuit, first in series and then in parallel. A potential difference is applied in the positions shown, and the voltage increased incrementally until one of the two wires begins to glow.

Explain which metal strip will glow first

In a thought experiment a teacher asks students to imagine an electron passing through a cell with a terminal voltage of 9 V.

The electron passes along a wire until it reaches the positive terminal of the cell. In the thought experiment, students are asked to assume that there is no obstruction to the movement of the electron within the wire.

Using energy considerations, calculate the final speed of the electron.

The teacher points out that the thought experiment is fundamentally flawed, since it breaks a certain law of physics.

Explain the teacher's comment, and hence use a simple observation from daily experience to prove that the teacher is correct.

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.