recall and use Q = It

Electric Current

Learning Objective

Recall and use the relationship \$Q = I t\$ to calculate charge, current or time in a variety of contexts.

Key Concepts

• Electric charge (\$Q\$) – the quantity of electricity. Measured in coulombs (C).
• Electric current (\$I\$) – the rate of flow of charge past a point. Measured in amperes (A), where \$1\ \text{A}=1\ \text{C s}^{-1}\$.
• Time (\$t\$) – the duration for which the current flows. Measured in seconds (s).
• The fundamental relationship: \$Q = I t\$

Units and Conversions

Deriving the Formula

The definition of current is the amount of charge passing a point per unit time:

\$I = \frac{Q}{t}\$

Re‑arranging gives the form most useful for calculations:

\$Q = I t\$

or

\$t = \frac{Q}{I}\$

Typical Applications

1. Finding the total charge transferred by a battery over a given period.
2. Determining how long a fuse will blow when a specified over‑current flows.
3. Calculating the charge required to produce a known amount of electrolysis.
4. Estimating the capacity of a capacitor in coulombs from its current‑time profile.

Worked Example

Problem: A 2.0 A lamp is switched on for 3.5 minutes. Calculate the total charge that passes through the lamp.

Solution:

1. Convert time to seconds: \$t = 3.5\ \text{min} \times 60\ \frac{\text{s}}{\text{min}} = 210\ \text{s}\$.
2. Use \$Q = I t\$: \$Q = (2.0\ \text{A})(210\ \text{s}) = 420\ \text{C}.\$

The lamp transfers \$420\ \text{C}\$ of charge while it is on.

Common Mistakes to Avoid

• Forgetting to convert minutes or hours to seconds before using the formula.
• Mixing up the symbols: \$I\$ is current, \$Q\$ is charge, \$t\$ is time.
• Assuming the current is constant when it actually varies; in such cases, integrate \$Q = \int I\,dt\$.
• Using the wrong unit prefixes (e.g., treating 5 mA as 5 A).

Practice Questions

1. A current of \$0.75\ \text{A}\$ flows for \$2\ \text{h}\$. Calculate the charge transferred in coulombs and in milli‑coulombs.
2. A device requires \$1.2\ \text{C}\$ of charge to operate. If it draws a current of \$0.3\ \text{A}\$, how long must it be switched on?
3. A fuse is rated at \$5\ \text{A}\$. If a short‑circuit causes a current of \$25\ \text{A}\$, how much charge passes through the fuse in the first \$0.2\ \text{s}\$? Will the fuse blow if it melts after \$10\ \text{C}\$ of charge?

Suggested Diagram

Summary

The equation \$Q = I t\$ links three fundamental electrical quantities. Mastery of this relationship enables you to solve a wide range of problems involving charge transfer, device operation times, and safety considerations such as fuse ratings.