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

Quantity	Symbol	SI Unit	Common Multiples
Charge	$Q$	coulomb (C)	1 C = $10^{6}$ µC, 1 C = $10^{3}$ mC
Current	$I$	ampere (A)	1 A = $10^{3}$ mA, 1 A = $10^{6}$ µA
Time	$t$	second (s)	1 min = 60 s, 1 h = 3600 s

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.