How Do You Calculate Electric Current (I = Δq/Δt)?

For both SL and HL, calculate electric current by dividing the charge passing a point by the time taken: $I=\frac{\Delta q}{\Delta t}$. Charge must be in coulombs and time in seconds to obtain current in amperes.

The Reasoning

Electric current is the rate of flow of electric charge. In the equation

$$I=\frac{\Delta q}{\Delta t},$$

$\Delta q$ means the amount of charge transferred during the time interval $\Delta t$. The symbol $\Delta$ means “change in,” not multiplication.

The equation gives the average current over the chosen interval. In a metallic conductor, mobile electrons carry charge, although conventional current is defined in the direction that positive charge would move. A larger transferred charge in the same time gives a larger current; the same charge transferred over a longer time gives a smaller current.

Since current is charge transferred per unit time,

$$1\text{ A}=1\text{ C s}^{-1}.$$

Worked Example

Suppose $24\text{ C}$ of charge passes through a wire in $6.0\text{ s}$:

$$I=\frac{\Delta q}{\Delta t}=\frac{24}{6.0}=4.0\text{ A}.$$

Therefore, the current is $4.0\text{ A}$.

Unit conversion is often the main challenge. If $600\text{ mC}$ passes in $3.0\text{ s}$, first convert $600\text{ mC}=0.600\text{ C}$. Then $I=0.600/3.0=0.200\text{ A}$. Substituting 600 directly would produce an answer 1000 times too large.

You may also rearrange the equation:

$$\Delta q=I\Delta t \qquad \text{and} \qquad \Delta t=\frac{\Delta q}{I}.$$

For example, $2.5\text{ A}$ flowing for $8.0\text{ s}$ transfers $20\text{ C}$.

A common misconception is that current is “used up.” Current is not consumed: components transfer electrical energy, while charge is conserved. In a series circuit, current is therefore the same at every point.

IB Exam Technique

For a Calculate question in B.5 Current and circuits, show the equation, substitution, and final answer. Convert prefixes before substituting and include the unit $\text{A}$. Keep unrounded intermediate values, then report sensible significant figures.