Heating Effect of Electric Currents (DP IB Physics: HL)

Deborah is an aspiring electrical engineer who sets out to investigate the resistivity of a metal wire. The material of the wire is unknown.

She measures the diameter of the wire using a micrometer screw gauge and takes a reading from the main scale and micrometer scale.

Determine the cross-sectional area of Deborah’s wire. 

Deborah then uses an ohmmeter to measure the resistance R for different lengths L of the wire.

Use Deborah’s measurements to complete the final column in the table and then determine the resistivity of the wire.

Suggest and explain two improvements to Deborah’s experimental method that would reduce the uncertainty in the final value of resistivity. 

Deborah swaps the sample of wire used in her experiment for a thin film of carbon.

Calculate the current which passes through the carbon film in the diagram for an applied voltage of 2.5 mV.

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.

Use Kirchhoff’s junction law to deduce an equation 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.

The terminals of the 5 V cell are reversed, and the variable resistor is set to a resistance of 5 Ω.

Using the current directions indicated, write:

Hence, calculate the power dissipated in .

A circuit containing four resistors is connected to a 12 V power supply.

Show that the potential difference between X and Y is 1 V.

A wire joins X and Y in the circuit.

Assuming current flows anticlockwise from the power supply, state and explain the direction of current along the line XY.

Another potential divider circuit includes a thermistor with 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, giving your answer to an appropriate number of significant figures.

For temperatures higher than room temperature, describe and explain how the power dissipated varies across:

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.

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.