Resistivity (CIE A Level Physics)

Two wires P and Q made of the same material are connected to the same electrical supply.

 P has twice the length of Q and one-third of the diameter of Q, as shown in the diagram.

What is the ratio   ?

In the circuit below, the reading V_T on the voltmeter changes from high to low as the temperature of the thermistor changes. The reading V_L on the voltmeter changes from high to low as the level of light on the light-dependent resistor (LDR) changes.

The readings V_T and V_L are both high.

 What are the conditions of temperature and light level ?

	Temperature	Light level
A B C D	low low high high	low high low high

In a fire alarm system, a thermistor T has a resistance of 2000 Ω at room temperature. Its resistance decreases as the temperature increases. The alarm is triggered when the potential difference between X and Y reaches 4.5 V.

What is the resistance of the thermistor when the alarm is triggered ?

Two electrically-conducting cylinders X and Y are made from the same material.

Their dimensions are as shown.

The resistance between the ends of each cylinder is measured.

 What is the ratio  ?

The graph shows the variation with length l of resistance R for two wires X and Y made from the same material.

What does the graph show?

A light-dependent resistor R has a resistance of about 1 MΩ in the dark and about 1 kΩ when illuminated. It is connected in series with a 5 kΩ resistor to a 1.5 V cell of negligible internal resistance.

The light-dependent resistor is illuminated (in an otherwise dark room) by a flashing light.

 Which graph best shows the variation with time t of potential difference V across R ?

Tensile strain may be measured by the change in electrical resistance of a strain gauge.

 A strain gauge consists of folded fine metal wire mounted on a flexible insulating backing sheet.

 The strain gauge is firmly attached to the specimen, so that the strain in the metal wire is always identical to that in the specimen.

When the strain in the specimen is increased, what happens to the resistance of the wire?

The resistance of a thermistor depends on its temperature, and the resistance of a light-dependent resistor (LDR) depends on the illumination.

 Under which conditions will the resistance of both a thermistor and an LDR be highest ?

	Thermistor	LDR
A B C D	highest temperature highest temperature lowest temperature lowest temperature	highest illumination lowest illumination highest illumination lowest illumination

A researcher has two pieces of copper of the same volume. All of the first piece is made into a cylindrical resistor P of length x.

All of the second piece is made into uniform wires each of the same length x which he connects between two bars of negligible resistance to form a resistor Q.

How do the electrical resistances of P and Q compare ?

Two wires have the same length and the same resistance. Wire X is made of a metal of resistivity 1.7 × 10^–8 Ωm, and wire Y is made of a metal of resistivity 5.6 × 10^–8 Ωm.

 The diameter of wire X is 0.315 mm.

 What is the diameter of wire Y?

A thermistor and another component are connected to a constant voltage supply. A voltmeter is connected across one of the components. The temperature of the thermistor is then reduced, but no other changes are made.

 In which circuit will the voltmeter reading increase ?

A copper wire is to be replaced by an aluminum alloy wire of the same length and resistance.

 Copper has half the resistivity of the alloy.

 What is the ratio   ?

The current in a block of semiconductor is 30.0 mA when there is a potential difference (p.d.) of 10.0 V across it. The dimensions of the block and the direction of the current in it are as shown.

The electrical meters used are accurate to ± 0.1 mA and ± 0.1 V. The dimensions of the block are accurate to ± 0.2 mm.

 What is the resistivity of the semiconductor?

The resistance of a metal cube is measured by placing it between two parallel plates, as shown.

The cube has volume V and is made of a material with resistivity ρ. The connections to the cube have negligible resistance.

Which expression gives the electrical resistance of the metal cube between X and Y? 

A wire PQ is made of three different materials, with resistivities ρ, 2ρ and 3ρ. There is a current I in this composite wire, as shown.

Which graph best shows how the potential V along the wire varies with distance x from P ?

A strain gauge consists of a length of wire with a uniform cross-sectional area. Its resistance is 2.50 kΩ. It is attached to a large pipe.

 When the pipe expands, the strain gauge changes in dimensions, such that the length increases by 4% and the diameter reduced by 1%.

 What is the new resistance of the strain gauge?

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

The thermistor is connected into the circuit shown below.

The battery has an e. m .f. of 9.0 V and negligible internal resistance. The voltmeter has infinite resistance.

 What is the temperature of the thermistor when the reading on the voltmeter is 4.0 V?

A conducting liquid fills a cylinder metal case to a depth y as shown in the diagram.

The resistance between the case and the metal rod is

The following strain gauge consists of a fine metal wire, so that an applied tension on the strain gauge results in changes in the length and cross-sectional area of the wire.

When the length of the wire is stretched by 5%, what is the percentage change in the resistance of the wire? Assume that the volume of a wire remains constant when it is stretched.

Aluminum and copper rods are designed to have the same length and the same resistance.

 The resistivity of copper is half that of aluminum, but its density is three times that of aluminum.

 Determine the ratio of the mass of the aluminum rod to the mass of the copper rod.