Resistivity (CIE AS Physics)

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.

A student investigates the resistivity ρ of a length of a wire l, with resistance R, diameter d and a potential difference V through it. 

Determine the resistivity, in terms of ρ, of a wire of the same length with a diameter 2d and a potential difference 3V through it instead.

The student decides to investigate how the cross-sectional area of a wire affects its resistance. The circuit they use to carry out the experiment is shown in Fig 1.1.

Fig 1.1

Describe a method to accurately determine the cross-sectional area of the wires.

The student uses three pieces of nichrome wire, each 1.5 m long. The cross-sectional area of the pieces of wire are

0.45 m²           0.21 m²           0.89 m²

Sketch a graph of voltage V against the current I for each of the wires.

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.

State and explain the assumption that is necessary for calculating the answer to part (a). 

In electrical power transmission conventional copper wires are often replaced with wires which conduct with wires with an effective resistance which is close to zero, called superconducting wires.

Explain why the superconducting wires increase the efficiency of electrical power transmission.

A wire of cross-sectional area A is from made metal of resistivity ρ. The wire is extended. Assume that the volume V of the wire remains constant as it extended.

Sketch on Fig 1.1 how the resistance R of the extending wires varies with the length l.

Two resistors X and Y have resistance R_X and R_Y respectively. The resistors are connected in series with a battery with electromotive force (e.m.f) E and zero internal resistance, as shown in Fig 1.1.

Fig 1.1

The resistors are made from metal wires. Data from the resistors are given in Table 1.1.

resistor	X	Y
diameter of metal
length of metal
resistivity of metal

Use information from Table 1.1 to determine the ratio

 

Show that the product of the ratio of X and Y connected in series and connected in parallel is 1.

Thin films of carbon are sometimes used in electronic systems. Typical dimensions of such a film are shown in Fig. 1.1.

Fig. 1.1.

Calculate the current which passes through the carbon film in Fig. 1.1. 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 Fig. 1.2.

Fig. 1.2.

Show that the current is approximately a million times larger if it is directed through the carbon film as shown in Fig. 1.2.

A tensile force is applied to the carbon film as shown in Fig. 1.2 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.