Resistance & Resistivity — Structured Questions (Cambridge International A-Level Physics): Exam Questions

A straight wire of unstretched length L has an electrical resistance R. The area of the cross-section *A *of the wire may be assumed to be constant.

State the relation between R, L, A and the resistivity *ρ *of the material of the wire.

Measurements made for a sample of metal wire are shown in Table 1.1.

Table 1.1

State the most appropriate instrument to use to measure

(i) the resistance of the wire

(ii) the diameter of the wire

(iii) the length of the wire.

Extract:

Measurements made for a sample of metal wire are shown in Table 1.1. Table 1.1 - resistance: 6.1 Ω; diameter: 0.44 mm; length: 1390 mm

Show that the resistivity of the metal is 6.67 × 10^–7 Ω m.

Extract:

Measurements made for a sample of metal wire are shown in Table 1.1. Quantity: resistance 6.1 Ω, diameter 0.44 mm, length 1390 mm.

State and explain what would happen to the resistivity of the wire if the diameter was doubled.

On Fig 1.1, sketch the change in resistance with temperature for a thermistor.

Fig 1.1

At 20 °C a wire is used to create a thermistor and has an electrical resistivity of 5.6 × 10^–8 Ω m.

State and explain what would happen to the resistivity of the thermistor if its temperature is increased to 60 °C.

(i) State the meaning of LDR.

(ii) On Fig 1.2, sketch the change in resistance with light intensity for an LDR.

Fig 1.2

Extract:

On Fig 1.2, sketch the change in resistance with light intensity for an LDR. A graph of the change in resistance with light intensity for an LDR should look like: Curved line showing decreasing gradient with greater light intensity; Smooth line not touching light intensity axis AND no horizontal or vertical line anywhere.

An LDR is connected to a circuit to operator an automatic street light. The resistance of the LDR is measured to be 5 kΩ at one time and 20 MΩ at another.

State which resistance the LDR is likely to be at during the day and which it will be at night.

Complete Table 1.1 by placing a tick (✓) in the correct column to show whether each of the quantities affects or does not affect the resistance of a conducting wire.

Table 1.1

A lamp is designed to take a current of 0.65 A when connected across a 24 V mains supply.

The filament is made from one of the three metals from Table 1.2 with a diameter of 66 µm.

Table 1.2

Calculate the cross-sectional area of the metal wire.

Extract:

A lamp is designed to take a current of 0.65 A when connected across a 24 V mains supply.

Calculate the resistance of the wire.

Extract:

A lamp is designed to take a current of 0.65 A when connected across a 24 V mains supply. The filament is made from one of the three metals from Table 1.2 with a diameter of 66 µm. Table 1.2: Nichrome resistivity 1.1 × 10^–6 Ω m; Tungsten resistivity 5.5 × 10^–7 Ω m; Copper resistivity 1.7 × 10^–8 Ω m. Cross-sectional area A = 3.421 × 10^–9 m². Resistance R = V/I = 24/0.65 = 36.9 Ω.

Hence, or otherwise, determine which metal the filament is made from for a length of 23 cm.

The photograph shows a statue of Buddha in Sri Lanka, which is protected by a lightning conductor.

During a storm, a potential difference of 2.7 MV was generated between a cloud and the top of the lightning conductor on the statue. A flash of lightning passed between the cloud and the lightning conductor, producing a current of 25 kA for a time of 7.5 ms.

Calculate the energy transferred by the lightning strike.

Energy transferred = ............................................

The lightning conductor is made from copper.

Sketch an *I–V *graph for the rod when it conducts a lightning strike to earth

Extract:

The lightning conductor is made from copper. Sketch an I–V graph for the rod when it conducts a lightning strike to earth (The rod will get hot since copper wires get hot, therefore) it is the equivalent of a non-ohmic resistor / filament lamp

Explain any changes which the lightning rod would undergo during a lightning strike.

Fig. 1.1. shows the graph of V against I for a non-ohmic conductor.

Fig. 1.1.

Calculate the maximum resistance of the lamp over the range shown by the graph.

Using the axes in Fig. 1.2. sketch the graph of current against potential difference for a diode.

Fig. 1.2.

For the graph in Fig. 1.3. determine

Fig. 1.3.

(i) the resistance when current = 10 mA

(ii) the power when current = 10 mA

An electrical component has the I-V characteristic shown in Fig. 1.1.

Fig. 1.1

Determine the resistance of the component when a potential difference of 6.0 V is applied across it.

Extract:

An electrical component has the I-V characteristic shown in Fig. 1.1. Fig. 1.1

For the component in part (a) calculate the minimum value of R as the potential difference across it changes over the range 0-10 V.

Extract:

An electrical component has the I-V characteristic shown in Fig. 1.1. Fig. 1.1 (I-V graph of the component).

For the component in part (a) calculate

(i) The power dissipated when V = 2.0 V

(ii) The maximum power dissipated before the component heats up

(iii) The value of resistance at the point identified in part (ii)

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

Extract:

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

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

Extract:

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

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

Extract:

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. [Answer: L = 6.4 m (2 s.f.)]

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.

Extract:

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.

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

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.

Extract:

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 mm^2^. 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.

Fig 1.1

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.

Table 1.1

Use information from Table 1.1 to determine the ratio

$\frac{powerdissipatedinY}{powerdissipatedinX}$

Extract:

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

Table 1.1 resistor | X | Y resistivity of metal | ρ/3 | ρ length of metal | 2l | l diameter of metal | 4d | d

Use information from Table 1.1 to determine the ratio (power dissipated in Y)/(power dissipated in X). The answer for the series arrangement is: (P_Y/P_X)_series = 24.

Show that the product of the ratio $\frac{powerdissipatedinY}{powerdissipatedinX}$ 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

Extract:

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

From (a): Current when directed horizontally, I_A = 3.3 × 10^–4 A. Length which current passes through, L = 3.0 × 10^–3 m; Cross-sectional area of conductor, A = (8.0 × 10^–3) × (2.0 × 10^–6) = 1.6 × 10^–8 m^2.

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.

Extract:

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. The length that the current passes through, L = 2.0 × 10^–6 m AND the cross-sectional area of conductor, A = (8.0 × 10^–3) × (3.0 × 10^–3) = 2.4 × 10^–5 m^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.