Physics A Level
Chapter 8: Electric current 8.2 Electric current
Physics A Level
Chapter 8: Electric current 8.2 Electric current
You will have carried out many practical activities involving electric current. For example, if you connect a wire to a cell (Figure 8.5), there will be current in the wire. And of course you make use of electric currents every day of your life – when you switch on a lamp or a computer, for example.
In the circuit of Figure 8.5, the direction of the current is from the positive terminal of the cell, around the circuit to the negative terminal. This is a scientific convention: the direction of current is from positive to negative, and hence the current may be referred to as conventional current. But what is going on inside the wire?
A wire is made of metal. Inside a metal, there are negatively charged electrons that are free to move about. We call these conduction or free electrons, because they are the particles that allow a metal to conduct an electric current. The atoms of a metal bind tightly together; they usually form a regular array, as shown in Figure 8.6. In a typical metal, such as copper or silver, one or more electrons from each atom breaks free to become conduction electrons. The atom remains as a positively charged ion. Since there are equal numbers of free electrons (negative) and ions (positive), the metal has no overall charge – it is neutral.
When the cell is connected to the wire, it exerts an electrical force on the conduction electrons that makes them travel along the length of the wire. Since electrons are negatively charged, they flow away from the negative terminal of the cell and towards the positive terminal. This is in the opposite direction to conventional current. This may seem a bit strange; it happens because the direction of conventional current was chosen long before anyone had any idea what was going on inside a piece of metal carrying a current. If the names positive and negative had originally been allocated the other way round, we would now label electrons as positively charged, and conventional current and electron flow would be in the same direction.
Note that there is a current at all points in the circuit as soon as the circuit is completed. We do not have to wait for charge to travel around from the cell. This is because the charged electrons are already present throughout the metal before the cell is connected.
We can use the idea of an electric field to explain why charge flows almost instantly. Connect the terminals of a cell to the two ends of a wire and we have a complete circuit. The cell produces an electric field in the wire; the field lines are along the wire, from the positive terminal to the negative. This means that there is a force on each electron in the wire, so each electron starts to move and the current exists almost instantly.
Sometimes a current is a flow of positive charges–for example, a beam of protons produced in a particle accelerator. The current is in the same direction as the particles. Sometimes a current is due to both positive and negative charges – for example, when charged particles flow through a solution. A solution that conducts is called an electrolyte and it contains both positive and negative ions. These move in opposite directions when the solution is connected to a cell (Figure 8.7). These charged particles are known as charge carriers. If you consider the structure of charged particles you will appreciate that charge comes in definite sized ‘bits’; the smallest bit being the charge on an electron or on a single proton. This ‘bittiness’ is what is meant when charge is described as being quantised.
1) Look at Figure 8.7 and state the direction of the conventional current in the electrolyte (towards the left, towards the right or in both directions at the same time?).
2) Figure 8.8 shows a circuit with a conducting solution having both positive and negative ions.
a: Copy the diagram and draw in a cell between points A and B. Clearly indicate the positive and negative terminals of the cell.
b: Add an arrow to show the direction of the conventional current in the solution.
c: Add arrows to show the direction of the conventional current in the connecting wires.
When charged particles flow past a point in a circuit, we say that there is a current in the circuit.
Electrical current is measured in amperes (A). So how much charge is moving when there is a current of $1 A$? Charge is measured in coulombs (C). For a current of $1 A$, the rate at which charge passes a point in a circuit is $1 C$ in a time of $1 s$. Similarly, a current of $2 A$ gives a charge of $2 C$ in a time of $1 s$. A current of $3 A$ gives a charge of $6 C$ in a time of $2 s$, and so on. The relationship between charge, current and time may be written as the following word equation:
$current = \frac{{charge}}{{time}}$
This equation explains what we mean by electric current.
The equation for current can be rearranged to give an equation for charge:
$charge = current \times time$
The unit of charge is the coulomb.
In symbols, the charge flowing past a point is given by the relationship:
$\Delta Q = I\Delta t$
where $\Delta Q$ is the charge that flows during a time $\Delta t$, and I is the current.
Note that the ampere and the coulomb are both SI units; the ampere is a base unit while the coulomb is a derived unit (see Chapter 3).
3) The current in a circuit is $0.40 A$. Calculate the charge that passes a point in the circuit in a period of 15 s.
4) Calculate the current that gives a charge flow of $150 C$ in a time of $30 s$.
5) In a circuit, a charge of $50 C$ passes a point in $20 s$. Calculate the current in the circuit.
6) A car battery is labelled $'50\,Ah'$. This means that it can supply a current of $50 A$ for one hour.
a: For how long could the battery supply a continuous current of $200 A$ needed to start the car?
b: Calculate the charge that flows past a point in the circuit in this time.
Because electric charge is carried by particles, it must come in amounts that are multiples of e. So, for example, $3.2 \times {10^{ - 19}}C$ is possible, because this is $ + 2e$, but $2.5 \times {10^{ - 19}}C$ is impossible, because this is not an integer multiple of e.
This reinforces the idea that charge is quantised; it means that it can only come in amounts that are integer multiples of the elementary charge. If you are studying chemistry, you will know that ions have charges of $ \pm e,2 \pm e$, etc. The only exception is in the case of the fundamental particles called quarks, which are the building blocks from which particles such as protons and neutrons are made. These have charges of $ \pm 1/3e$ or $ \pm 2/3e$ . However, quarks always appear in twos or threes in such a way that their combined charge is zero or a multiple of e.
7) Calculate the number of protons that would have a charge of one coulomb. ($\Pr oton\,charge\, = \, + 1.6 \times {10^{ - 19}}C$.)
8) Which of the following quantities of electric charge is possible? Explain how you know.
$6.0 \times {10^{ - 19}}C,\,8.0 \times {10^{ - 19}}C\,,\,10.0 \times {10^{ - 19}}C$