4.1.1 - Charge, current and Kirchhoff's first law

Charge and coulombs

Electric charge is a physical quantity. It can be positive, negative or zero, and its SI unit is the coulomb, symbol $\mathrm{C}$.

At this stage, do not think of charge as a continuous liquid that can be divided into any size. At particle level, charge comes in packets. The size of the smallest charge magnitude used in this lesson is the elementary charge, $e$.

The net charge on a particle or object is quantised. That means its net charge must be a whole-number multiple of $e$, such as $0$, $+e$, $-e$, $+2e$ or $-3e$.

Here $Q$ is the net charge in coulombs, $N$ is a whole number, and $e$ is the elementary charge. The sign tells you whether the object has a net positive or negative charge.

Worked example: a small object has net charge $-6.40 \times 10^{-19}\,\mathrm{C}$. How many excess electrons does it have?

Use the magnitude of the charge:

The negative sign means the object has excess electrons, so it has $4$ excess electrons. A result such as $4.5$ excess electrons would tell you that the data or assumption is not physically possible for a net charge made from whole elementary charges.

The key point is that coulombs are the unit used in calculations, while $e$ is the charge packet used to connect charge to individual particles.

Current as charge flow

Electric current tells you the rate at which charge passes a point. A larger current means more charge passes the point each second.

The OCR data booklet gives the relationship in the form:

Here $\Delta Q$ is the charge that passes a point in coulombs, $I$ is the current in amperes, and $\Delta t$ is the time interval in seconds. The same relationship can be rearranged as:

The ampere is therefore equivalent to $\mathrm{C\,s^{-1}}$: a current of $1\,\mathrm{A}$ means $1\,\mathrm{C}$ of charge passes each second.

Worked example: a steady current of $0.48\,\mathrm{A}$ flows for $25\,\mathrm{s}$. Calculate the charge that passes a point, then estimate the number of elementary charges this represents.

First calculate the charge flow:

Then divide by the elementary charge:

So $12\,\mathrm{C}$ is about $7.5 \times 10^{19}$ elementary charges. That large number is normal: a coulomb is a very large amount of charge on the particle scale.

When using this equation, convert time into seconds before substituting. A common OCR-style slip is to put minutes directly into the equation and make the current or charge too small by a factor of $60$.

In practical circuit work, current is measured with an ammeter or multimeter in the current path, and the reading should be recorded in amperes with sensible significant figures. Detailed circuit construction belongs to later OCR circuit lessons; here, the important idea is that the meter is measuring charge flow per second.

For a finite interval, $I=\Delta Q/\Delta t$ gives the mean current during that interval. If current is steady, $Q=It$. If it varies, the gradient of a charge–time graph gives current: a steeper graph means a greater rate of charge flow. Use a tangent for the current at a particular instant and a chord for the mean over an interval.

Charge carriers and direction

Current is always charge flow, but the moving charged particles are not always the same.

In metals, the mobile charge carriers are electrons. They have negative charge, so their drift direction is opposite to the direction chosen for conventional current.

In electrolytes, charge is carried by ions. Positive ions and negative ions can both move, and their contributions together make an electric current through the liquid or solution.

The direction convention is useful because it lets physicists analyse circuits consistently without first asking what the charge carrier is. It is not claiming that electrons are positive. It is a sign convention: electron flow in a metal is opposite to conventional current because electrons carry charge $-e$.

Two misconceptions are worth clearing away now. First, current is not the same thing as energy transfer; it is charge flow. Second, current in a metal is not electrons racing around the circuit at light speed. The taught model here is steady drift of charge carriers, not a high-speed stream of individual particles completing the loop instantly.