Q1:
A wire made of an unknown substance has a resistance of 125 mΩ. The wire has a length of 1.8 m and a cross-sectional area of m2. What is the resistivity of the substance from which the wire is made? Give your answer in scientific notation to one decimal place.
- A Ω⋅m
- B Ω⋅m
- C Ω⋅m
- D Ω⋅m
- E Ω⋅m
Q2:
A copper wire with a resistance of 12.8 mΩ has a cross-sectional area of m2. Find the length of the wire. Use Ω⋅m for the resistivity of copper. Give your answer to one decimal place.
Q3:
A copper wire is 2.5 m long and has a cross-sectional area of m2. Find the resistance of the wire. Use Ω⋅m for the resistivity of copper.
Q4:
Which of the following formulas correctly relates the resistivity, , of a substance to the resistance of an object with a length, , that is made of the substance if the object has a cross-sectional area and a resistance ?
- A
- B
- C
- D
Q5:
A copper wire with a resistance of 22 mΩ has a length of 6.2 m. Find the cross-sectional area. Use Ω⋅m for the resistivity of copper. Give your in scientific notation to one decimal place.
- A m2
- B m2
- C m2
- D m2
- E m2
Q6:
A current of 1.4 A in a copper wire is carried by free electrons. The cross-sectional area of the wire is m2. Find the average speed at which free electrons pass through the wire. Use a value of C for electron charge and a value of m−3 for the density of free electrons in copper. Give your answer in scientific notation to one decimal place.
- A m/s
- B m/s
- C m/s
- D m/s
- E m/s
Q7:
The wires that carry current from a power station to a substation are 7.25 km long. They are made of copper with a resistivity of Ω⋅m. The current through the wires is 450 mA. The power dissipated by the wires is required to be no more than 15 W. What is the minimum cross-sectional area required for the wires that transmit the current? Give your answer in scientific notation to one decimal place.
- A m2
- B m2
- C m2
- D m2
- E m2
Q8:
A current of 77 mA in a conducting wire of an unknown material is carried by free electrons. The cross-sectional area of the conductor is m2. Find the density of free electrons in the material if the average speed of the free electrons along the wire is 0.18 mm/s. Use a value of C for the electron charge. Give your answer in scientific notation to one decimal place.
- A m−3
- B m3
- C m−3
- D m−3
- E m−3
Q9:
If a cylindrical metallic rod of cross-sectional area 3 cm2 and resistance 10 Ω is pulled uniformly until its cross-sectional area becomes 1.5 cm2, then the resistance of the rod is .
- A 40 Ω
- B 2.5 Ω
- C 5 Ω
- D 20 Ω
Q10:
Diagrams (a) and (b) show sections of identical conducting materials consisting of three equally separated ions. Free electrons which have a velocity greater than a velocity move away from the nearest ion to a neighbouring ion. Free electrons with velocities lower than do not move to a neighbouring ion. Diagram (c) shows a section of a conducting material consisting of three equally separated ions. The charge of each of these ions is the same as the charge of each of the ions in diagrams (a) and (b).
Which of the following statements correctly describes how the velocity of electrons required for them to move between ions in the material in diagram (c) compares to the velocity of electrons required for them to move between ions in the material in diagrams (a) and (b)?
- A The velocity of electrons required in diagram (c) is greater than the velocity of electrons required in diagrams (a) and (b).
- B The velocity of electrons required in diagram (c) is lower than the velocity of electrons required in diagrams (a) and (b).
- C The velocity of electrons required in diagram (c) is equal to the velocity of electrons required in diagrams (a) and (b).
Which of the following statements correctly describes how the resistivity of the material in diagram (c) compares to the resistivity of the material in diagrams (a) and (b)?
- A The resistivity of the material in diagram (c) is greater than the resistivity of the material in diagrams (a) and (b).
- B The resistivity of the material in diagram (c) is lower than the resistivity of the material in diagrams (a) and (b).
- C The resistivity of the material in diagram (c) is equal to the resistivity of the material in diagrams (a) and (b).
Q11:
Diagrams (a) and (b) show identical sections of two conducting objects made from the same material. The temperature of the material in diagram (b) is much higher than the temperature of the material in diagram (a). The free electrons move in a conductor and collide with the atoms of the materials repeatedly, making the electrons’ paths appear nearly random. When an electric field is applied across the conductor, it causes the electrons to drift in the direction opposite to that of the electric field with a drift velocity .
Which of the following statements correctly describes how the resistivity of the material in diagram (a) compares to the resistivity of the material in diagrams (b)?
- A The resistivity of the material in diagram (a) is greater than the resistivity of the material in diagrams (b).
- B The resistivity of the material in diagram (a) is equal to the resistivity of the material in diagrams (b).
- C The resistivity of the material in diagram (a) is lower than the resistivity of the material in diagrams (b).
Q12:
Two conducting materials have the same length and resistance. One of them is made of aluminium with resistivity , and the other is made of copper with resistivity . What is the ratio between the radius of the aluminium wire and the radius of the copper wire ?
- A
- B
- C
- D
Q13:
The diagram shows two identical circuits. Each circuit’s conducting wire has had a section of it greatly magnified to show the ions that the conducting wire is comprised of and the free electrons that move between these ions. The sections have equal resistances. The dimensions of the sections are identical and the wires are uniform. In which wire do free electrons move from the negative terminal to the positive terminal at a greater average speed?
- A The wire containing section (b).
- B The wire containing section (a).
Q14:
The graph shown illustrates the relationship between the applied potential difference and the electric current intensity through two conducting wires, A and B, of the same material and length at a specific temperature. Which of the two wires has a larger cross-sectional area?
- A Wire B
- B Wire A
- C Both have the same cross section.
- D There is not enough information to determine.
Q15:
The diagram shows two identical circuits. Each circuit’s conducting wire has had a section of it greatly magnified to show the ions that the conducting wire is comprised of and the free electrons that move between these ions. The wires are uniform and the dimensions of the sections are identical. Which of the following statements most correctly compares the electrical characteristics of the magnified sections?
- A The sections are identical in all ways except for the time taken for free electrons to pass through the sections.
- B The sections are identical in all ways except for the number of free electrons per unit length of the sections, where length is the distance between the terminals of the circuit.
- C The sections differ in both of the ways mentioned.
Q16:
What is the mass of a wire that has a density of 7,000 kg/m3, a resistance of 5 Ω, a length of 1,000 cm, and a resistivity of Ω⋅m?
- A 0.014 kg
- B 0.00014 kg
- C 0.14 kg
- D 140 kg
Q17:
The diagram shows two identical circuits. Each circuit’s conducting wire has had a section of it greatly magnified to show the ions that the conducting wire is comprised of and the free electrons that move between these ions. The conducting wires are both made of the same substance. Which of the following statements most correctly compares the electrical characteristics of the magnified sections?
- A The sections are identical in all ways except for the number of free electrons per unit length of the sections, where length is the distance between the terminals of the circuit.
- B The sections are identical in all ways except for the time taken for free electrons to pass through the sections.
- C The sections differ in both of the ways mentioned.
Q18:
The diagram shows two identical circuits. Each circuit’s conducting wire has had a section of it greatly magnified to show the ions that the conducting wire is comprised of and the free electrons that move between these ions. The conducting wires are both made of substances with different resistivities. The wires are uniform. The number of free electrons crossing each section in a given time interval is the same for both sections. Which wire is made of the substance that has the greater resistivity?
- A The wire containing section (a).
- B The wire containing section (b).
Q19:
A conducting material that was in the form of a cube of side length 5 cm is reshaped to be a cylindrical wire of electric resistance 10 Ω. Calculate the length and the radius of the wire, knowing that the resistivity of the cube’s material is Ω⋅m.
- A 11 180 m, m
- B 11.18 m, m
- C 12 m, m
- D 353.55 m, m
Q20:
The given graph represents the dependence between the electric current intensity and the applied potential difference on the ends of two wires, A and B, of the same material. If both wires have the same length and the cross-sectional area of wire B is m2, then the cross-sectional area of wire A is . Give your answer in scientific notation to one decimal place.
- A m2
- B m2
- C m2
- D m2
Q21:
The given graph represents the dependence between the electric current intensity and the applied potential difference on the ends of two wires, A and B, of the same material. If both wires have the same cross-sectional area and the length of wire B is 9 m, then the length of wire A is .
- A m
- B 3 m
- C m
- D 9 m
Q22:
The graph below shows how the resistance, , of a conducting wire depends on its length, . Knowing that the cross-sectional area of the wire is 0.5 cm2, the resistivity of the wire’s material is equal to .
- A Ω⋅m
- B Ω⋅m
- C Ω⋅m
- D Ω⋅m
Q23:
A battery generates a potential difference of 5 V between the ends of a copper wire. Knowing that the wire has a length of 50 m, a cross-sectional area of m2, and a resistivity of Ω⋅m, the electric current intensity that is carried by this wire is . Give your answer to two decimal places.
- A 4.48 A
- B 0.18 A
- C 7.25 A
- D 5.59 A
Q24:
What happens to the resistance of an iron wire if its cross-sectional area is doubled and its length is halved?
- A It increases to its double.
- B It increases to its quadruple.
- C It decreases to its half.
- D It decreases to its quarter.
Q25:
The diagram shows two identical circuits. Each circuit’s conducting wire has had a section of it greatly magnified to show the ions that the conducting wire is comprised of and the free electrons that move between these ions. The conducting wires are uniform and are made of substances with different resistivities. The number of free electrons crossing each section in a given time interval is the same for both sections. Which wire is made of the substance that has the greater resistivity?
- A The wire containing section (a).
- B The wire containing section (b).
