Resistance & Resistivity (CIE A Level Physics)

The graph below shows the variation of the current I through a lamp with potential difference V across it.

Which of the following graphs best represents the variation of power P dissipated in the same lamp with I ² ?

Circuit contains three identical lamps A, B and C. Circuit also contains three switches, S₁, S₂ and S₃, as shown.

One of the lamps is faulty. In order to detect the fault, an ohm-meter is connected between terminals X and Y.

 When measuring resistance, the ohm-meter causes negligible current in the circuit. Readings of the ohm-meter for different switch positions are shown in the table.

Switch			Meter reading / Ω
S1	S2	S3
open closed open open	open open closed closed	open open open closed	∞ 15 30 15

Which lamps are faulty?

The current flowing through a component varies with the potential difference V across it as shown.

Which graph best represents how the resistance R varies with V ?

The circular cross-sectional area of a uniform metal wire varies along its length. There is a current in the wire. The narrow end of the wire is at a reference potential of zero.

Which graph best represents the variation with distance x along the wire of the potential difference V relative to the reference zero?

The graph shows the I -V characteristics of a semiconductor diode

A cell of e. m .f. 1.2 V and negligible internal resistance is connected in series to a semiconductor diode and a resistor R₁, as shown below

A resistor R₂ of resistance 375 Ω is connected across the cell. The diode has the characteristic shown in the graph. The current supplied by the cell is 7.6 mA.

 What is the resistance of R₁?

The graph shows how the current I varies with potential difference V for an electrical component.

Which row of the table gives the resistance of the component at V₂ and describes how the resistance changes from V₁ to V₂ ?

	Resistance at V2	Change in resistance from V1 to V2
A		increases
B		decreases
C		increases
D		decreases

The graph shows the relationship between potential difference V and current I for a fixed 20 Ω resistor and a filament lamp.

The resistor and lamp are placed in series with a 9 V battery of negligible internal resistance. What is the current in the circuit ?

The graphs show the I -V characteristics for a metal conductor and a thermistor

What is the ratio   ?

One style of light bulb, very different from the "incandescent" design which works on the principle of a super-heated wire filament emitting light, is called a gas discharge tube.

 In this design of light bulb, light is produced by the direct excitation of gas molecules as electric current passes between two electrodes.

What will the I - V graphs of these bulbs look like?

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.

A charge of 8.0 C passes through a resistor of resistance 30 Ω at a constant rate in a time of 20 s.

 What is the potential difference across the resistor?

The I -V characteristics of two electrical components P and Q are shown below.

Which statement is correct ?

The resistance R of a resistor is to be determined. The current I in the resistor and the potential difference V across it are measured.

 The results, with their uncertainties, are

                  I = (2.0 ± 0.2) A                     V = (15.0 ± 0.5) V

 What is the uncertainty in this value for R ?

The variation with potential difference V of the current I in a semiconductor diode is shown below.

What is the resistance of the diode for applied potential differences of +1.0 V and –1.0 V ?

 

	Resistance
	at +1.0 V	at –1.0 V
A B C D	20 Ω 20 Ω 0.05 Ω 0.05 Ω	infinite zero infinite zero

A battery of negligible internal resistance is connected to two 10 Ω resistors in series.

What charge flows through each of the 10 Ω resistors in 1 minute?

Two heating coils X and Y, of resistance R_X and R_Y respectively, deliver the same power when 12 V is applied across X and 6 V is applied across Y.

 What is the ratio   ?

A student found two unmarked resistors. To determine the resistance of the resistors, the circuit below was set up. The resistors were connected in turn between P and Q, noting the current readings.

 The voltage readings were noted without the resistors and with each resistor in turn.

The results were entered into a spreadsheet, as shown.

1.5	1.3	28	46
1.5	1.4	14	100

The student forgot to enter the column headings.

 Which order of the headings would be correct?

A	e.m.f / V V / V R / Ω I / mA
B	V / V e.m.f / V R / Ω I / mA
C	V / V e.m.f / V I / mA R / Ω
D	e.m.f / V V / V I / mA R / Ω

A 2 Ω resistor and a 4 Ω resistor are connected to a cell.

Which graph shows how the potential V varies with distance between X and Y ?

The diagram shows a length of track from a model railway connected to a battery, a resistor and a relay coil.

With no train present, there is a current in the relay coil which operates a switch to turn on a light.

 When a train occupies the section of track, most of the current flows through the wheels and axles of the train in preference to the relay coil. The switch in the relay turns off the light.

 Why is a resistor placed between the battery and the track?

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?