Charge and Current

Electrically charge particles exert a force on each other. The magnitude of this force is dependent on the charge on each particle. The magnitude of the force is inversely proportional to the square of the distance between particles.

The base unit of charge is the coulomb. One coulomb equals the charge of $6.24 \times 10^{18}$ electrons. In other words, a single electron has a charge of $1.6021 \times 10^{-19}$ coulombs. The symbol for charge is $Q$ or $q$.

Electric circuits move electrical charge around so that useful work is accomplished. These moving charges generate an electric current that we denote as $i$ or $I$. In other words, if $q(t)$ is the amount of charge at a specific point in space at time $t$, then the current passing through this point equals the first time derivative of $q$. In other words,

$$\begin{eqnarray*} i(t) = \frac{dq(t)}{dt} \end{eqnarray*}$$

The basic unit of current is the ampere (denoted with the abbreviation $A$). One ampere equals one coulomb of charge passing through a point in space over one second. In other words, one ampere equals one coulomb per second.

Consider a wire that has a current of $3$ amps passing across a specific point on that wire. The charge can either be moving from right to left or left to right. So to completely specify the nature of the current, we must also specify the direction in which the current is travelling. This is done by associating a sign to the current. In other words, current is a signed quantity.

The sign given to a current depends upon what we are interested in measuring. Moving charge can be thought of as either

• negatively charged electrons moving through the wire,
• or positively charged particles moving through the wire

In the first case, we have a so-called electron current. In the second case, we have a so-called conventional current. It is common practice to use conventional rather than electron currents. Throughout our work this is the convention we shall use.

In circuit diagrams, we denote the current flowing into a circuit element by an arrow labelling one of the device's terminals. The arrow is usually labelled with the size of the current. The standard convention (called the passive labelling convention) used in labelling these arrows is to use a positive number when then current is pushing positive charges into the device. If the number is negative, then the current is pulling positive charges out of the device. Figure 16 illustrates the passive labelling convention for a resistor.

Figure 16: Current Flow into Circuit Element

Recall that the number labelling the current is signed with an arrow. This means we can obtain two different labels for the same direction of conventional current. Figure 17 shows two such labels. In the first case, we are pushing positive charge from terminal $a$ into the device. In the second case, we are pulling positive charge from the device into terminal $b$. The end result for both labels is the same, namely that the flow of positive charges is from left to right through the device.

Figure 17: Two different labellings of the same current

The total charge entering a circuit element is obtained by integrating the differential equation $i(t)=dq(t)/dt$. Assume that the charge is initially $q(t_0)$, then the total charge entering the device between times $t_0$ and $t$ will be

$$q(t) - q(t_0) = \int_{t_0}^t i(\tau) d \tau$$