Chapter 8: Charge and Current

Question 1

1. Define electric current.
2. Give the defining equation for electric current.
3. What can you equate 1 A to?

Answer 1

1. Electric current is defined as the rate of flow of charge and is measured in amperes.
2. I = ΔQ / Δt
3. 1 A is the same as one coulomb of charge passing a given point per second.

Question 2

1. What is electric charge?
2. What are the units of charge?
3. How is the coulomb defined?
4. What is 1 C in base SI units?

Answer 2

1. Electric charge is a physical property, like mass or temperature. Objects with charges interact and exert forces on each other: like charges repel and opposite charges attract.
2. Electric charge is measured in coulombs (C).
3. The coulomb is defined as the electric charge flowing past a point in one second when there is an electric current of one ampere.
4. As ΔQ = I Δt, one coulomb = one ampere second (A s) in base units.

Question 3

What is the elementary charge?

Answer 3

• The elementary charge, equal to the charge on one proton, is 1.6 x 10^-19 C.
  
  • A proton has a charge of +1e and an electron has a charge of -1e.

Question 4

How can the number of electrons passing through a given point in a given time be calculated from the current in the wire?

Answer 4

1. From the value of the current in a metal wire, we can calculate the charge passing through it in a given time using I = ΔQ / Δt.
2. The number of electrons can then be calculated by dividing the charge passing through the wire by the elementary charge (1.6 x 10^-19 C).

Question 5

How can the size of the charge on a particular object be expressed in terms of its individual quanta?

Answer 5

• The size of the charge on a particular object can be expressed as a multiple of e. So the net charge on an object is given by: Q = ±ne
  where Q is the net charge on the object in coulombs, n is the number of elecrons, and e is the elementary charge.
• The charge on an object can be described as quantises because chatge only has certain values: multiple of e.

Question 6

How are charge carriers different from electrons? Give an example.

Answer 6

An electric current is a flow of any type of charge carrier — an electron is just one possibility. For example, in metals the charge carriers are electrons but in liquid the charge carriers tend to be ions.

Question 7

1. Describe the model of electric current in metals.
2. Describe one way to create a flow of charge.

Answer 7

1. Most electrons in metal atoms remain fixed to their atom, organised in a lattice structure of positive ions. However, these are surrounded by a number of free elecrons as a small number of electrons from each atom are delocalised. Note that the positive ions are not free to move, but they do vibrate around fixed points. They vibrate more vigorously as the temperature of the metal increases.
2. One way to create a flow of charge is to make one end of a wire positive and the other negative. The electrons in the metal wire will be attracted towards the positive end, and so move through the wire as an electric current.

Question 8

How can an electric current be made larger?

Answer 8

An electric current can be made larger twofold:

1. a greater number of electrons moving past a given point each second (e.g. a wire with greater cross-sectional area)
2. the same number of electrons moving faster through the metal.

Question 9

Describe and explain the use of conventional current. How is this different to electron flow?

Answer 9

• As current was discovered before the electron, conventional current is defined as the current from a positive terminal towards a negative one, regardless of the direction of the movement of the charge carriers.
  
  • Electrons actually travel from the negative terminal towards the positive terminal.

Question 10

1. What are electrolytes?
2. What physical state do electrolytes appear in?

Answer 10

1. Electrolytes are liquids that can carry an electric current. Here, the electric current is not a flow of electrons but a flow of ions.
2. All electrolytes are either molten ionic compounds or, more commonly, ionic solutions.

Question 11

1. How is electric current measured?
2. Why should you not have an ammeter with a high resistance?

Answer 11

1. An ammeter is used to measure the electric current at any point in a circuit. It is always placed directly in series in the circuit at the point where you want to measure the current.
2. As ammeters are placed in series, they should have the lowest possible resistance in order to reduce the effect they have on the current — an ammeter with high resistance would decrease the current is should be measuring.

Question 12

1. What is the conservation of charge?
2. State Kirchhoff’s first law.
3. How can Kirchhoff’s first law be deduced from the conservation of charge?

Answer 12

1. Conservation of charge states that electric charge can neither be created nor destroyed. The total amount of electric charge in the universe is constant.
2. Kirchhoff’s first law states that, for any point in an electric circuit, the sum of currents into that point is equal to the sum of currents out of that point: Σ I_in = Σ I_out.
3. The charge (measured in coulombs) is the product of the current (in amperes) and the time (in seconds). Thus as charge is conserved, electric current must also be conserved.

Question 13

1. What is the number density of a material?
2. How can materials be classified according to their number density? Explain.

Answer 13

1. The number density is the number of free electrons per cubic metre of material. The highest the number density, the better the material is at conducting electricity.
2. Materials can be classified into three groups according to their number density.
   
   • Conductors have a very high number density (to the order of 10²⁸ m^–3).
   • Semiconductors have a lower number density than conductors (to the order of 10¹⁷ m^–3). Therefore in order to carry the same current as conductors, the electrons in semiconductors need to move much faster. This increases the temperature of the semiconductor.
   • Insulators have the lowest number density and are therefore very bad electrical conductors.

Question 14

1. Why do electrons move slowly?
2. Explain how lights can turn on so quickly despite electrons moving slowly.

Answer 14

1. Electrons move slowly because free electrons repeatedly collide with the positive metal ions as they drift through the wire towards the positive terminal.
2. The reason that lights turn on so quickly is that all the free electrons in the wire start moving almost at once.

Question 15

Describe the individual terms and the use of the equation I = Anev.

Answer 15

• The equation I = Anev can be used for electric current.
  
  • I is the electric current of the conductor in amperes.
  • A is the cross-sectional of the conductor in m².
  • n is the number density
  • e is the elementary charge (1.60 x 10^–19 C)
  • v is the mean drift velocity of the charge carriers in m s^-1.

Question 16

Describe the effect of decreasing cross-sectional area of the wire in an electric circuit.

Answer 16

• In order to maintain the same current (rate of flow of charge), electrons/charge carriers must move faster through narrower wires.
• The mean drift velocity is inversely proportional to the cross-sectional area of the wire.