Resistance & Resistivity (AQA A Level Physics)

State what is meant by a superconducting material. Explain, therefore, why this material would be useful in improving the efficiency of power stations and hence reduce carbon dioxide emissions.

With the aid of a sketch graph, explain the term transition temperature.

Niobium has the highest transition temperature of any superconductor. 

Sketch on the axes in Figure 1 the variation of resistance with temperature for Niobium that becomes superconducting at 9.2 K. 

Figure 1

Explain why superconductors are useful for applications which require strong magnetic fields and name two such applications.

A cable consists of seven straight strands of copper wire each of radius 30 µm as shown in Figure 1. 

Figure 1

The cable is 1.5 m in length and has a resistance of 1.3 Ω. 

Calculate the resistance of one strand of copper wire.

Calculate the resistivity of copper and state an appropriate unit in your answer.

One strand of the wire is now stretched to three times its original length by a process that keeps its volume constant. 

If the resistivity of the copper wire remains constant, show that the resistance increases by 9R.

State one advantage of using a stranded cable rather than a solid core cable with copper of the same total cross-sectional area.

Explain the required conditions for a material to become superconducting.

Figure 1 shows the cross-sectional area of a cable consisting of parallel filaments that can be made superconducting, embedded in a cylinder of copper.

 Figure 1

The diameter of the copper in the cable is 0.48 mm. 

Calculate the resistance of 2.2 m length of the cable. 

            Resistivity of copper = 1.7 × 10^–8 Ωm

Explain, with a calculation, how the resistance would change for a copper wire in the cable with a diameter twice as wide as that in part (b).

State and explain what happens to the resistance of the cable when the embedded filaments of wire are made to be superconducting.

A thermistor is a type of sensory resistor commonly used in thermostats to control the central heating in houses. 

State how the resistance of a negative temperature coefficient (ntc) thermistor changes with temperature and explain why this occurs.

Figure 1 shows part of a miniature electronic circuit with two small resistors connected in parallel. 

The material from which each resistor is made has a resistivity of 2.6 × 10⁵ Ω m and both resistors have dimensions of 15 mm by 2.3 mm by 1.3 mm. 

Figure 1

Calculate the total resistance of the electronic circuit in MΩ.

The designer increases the size of the circuit including the base by making every dimension larger by a factor of 10. The potential difference across the resistors is unchanged. 

Show this increase in dimensions results in the resistance of each resistor decreasing by a factor of 10.

The resistors are replaced with wires with a circular cross-sectional area with diameter d and a resistance per unit length r. 

Sketch a graph of how the resistance per unit length r varies with diameter d of one of the wires.

An electrical heating element, made from uniform nichrome wire, is required to dissipate 600 W when connected to the 230 V mains supply. 

The radius of the wire is 0.16 mm. 

Calculate the length of nichrome wire required. 

            Resistivity of nichrome = 1.1 × 10^–6 Ω m

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

Explain why the resistivity of the nichrome wire changes with temperature.

An engineer wants to use the same uniform nichrome wire to use in another identical electrical heating element which is also required to dissipate 600 W when connected to the 230 V mains supply. 

The only nichrome wire they have available has a radius of 0.08 mm. 

Calculate the length needed for this new nichrome wire to produce the same current through the heating element.

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

Figure 1 shows the micrometer screw gauge she uses to measure the diameter of the wire.

Figure 1

Determine the resolution of the main scale and the micrometer scale as shown in Figure 1. 

Shareen measures the diameter of the wire using the micrometer screw gauge and takes a reading from the main scale and micrometer scale, which is shown in Figure 2.

Figure 2

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

Shareen then uses an ohmmeter to measure the resistance R for different lengths L of the wire. Her measurements are shown in Table 1 below: 

Table 1

 Determine the resistivity of the wire, including an appropriate unit. 

Use the additional column in Table 1 to record your answer.

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

Thin films of carbon are sometimes used in electronic systems. 

Typical dimensions of such a film are shown in Figure 1: 

Figure 1

Calculate the current which passes through the carbon film in Figure 1 for an applied voltage of 2.5 mV. 

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

The applied voltage is kept constant, but the current is now directed through the carbon film as shown in Figure 2: 

Figure 2

Show that the current is approximately a million times larger if it is directed through the carbon film as shown in Figure 2. 

A tensile force is applied to the carbon film as shown in Figure 2, in a plane that is normal to the current. 

Without performing any calculations, discuss how the resistance of the carbon film changes as a result of the applied tensile force.  

State any assumptions you make in your answer.

At room temperature a metal has a resistivity of 3.0 × 10^–7 Ω m. 

A 2.5 m length of wire made from this metal has a cross-sectional area of 0.50 mm². 

Calculate the power dissipated in this length of wire when it carries a current of 10 mA.

Explain the assumption that is necessary for calculating the answer to part (a).

The wire is cooled from room temperature θ_r and becomes superconducting. 

Sketch a graph on the axes provided in Figure 1 below to show how the wire’s resistivity would vary with temperature as it is cooled from room temperature θ_r. 

Include any appropriate labels on your sketch. 

Figure 1

Explain why the efficiency of electrical power transmission is improved when conventional copper wires are replaced with metal wires that are superconducting. 

Cables used in high-voltage power transmission typically consist of multiple wires. 

A cross-section of such a cable is shown in Figure 1: 

Figure 1

This cable consists of seven wires, each of diameter 7.4 mm. The central steel wire has a resistance per metre of 3.3 × 10^–3 Ω m^–1 and the surrounding aluminium wires each have a resistance per metre of 1.1 × 10^–3 Ω m^–1. 

By comparing the resistivity of aluminium and steel, show that about 5% of the total current flowing through the cable flows through the central steel wire. 

You should assume that each wire in the cable is connected to the same voltage supply.

The potential difference across a length of 1.0 km of the cable is 80 V. 

Calculate the total power loss for a 1.0 km length of cable.

A mechanical engineering student suggests the following: 

“The central steel wire should be replaced with another aluminium wire because aluminium has a lower resistivity. Hence, more current can be transmitted across long distances.” 

Comment on the student’s suggestion by comparing the properties of the steel and aluminium wires.