Physics 9702/12 — February/March 2018

Background Concept

Electric charge $Q$ is measured in coulombs (C). Two useful definitions connect charge to other electrical quantities:

1. Current is rate of flow of charge:

$$I = \frac{\Delta Q}{\Delta t} \quad \Rightarrow \quad Q = It$$

1. Potential difference is energy transferred per unit charge:

$$V = \frac{W}{Q}$$

where $V$ is in volts (V), $W$ is in joules (J), and $Q$ is in coulombs (C). This second definition is often the quickest way to rewrite the coulomb in terms of other derived units.

Understanding the Question

You are given four compound units and asked which one is equivalent to the coulomb. So we need to express $\text{C}$ in terms of the units appearing in the options (A, J, V, W) and see which matches.

Approach

Use the definition of potential difference:

$$V = \frac{W}{Q}$$

Rearrange to make $Q$ the subject. The resulting unit for $Q$ will be an expression involving joules and volts, which can be compared directly to the options.

Step-by-Step Reasoning

Start from

$$V = \frac{W}{Q}$$

Rearrange:

$$Q = \frac{W}{V}$$

So one coulomb is one joule per volt. Therefore the correct option is joule per volt, which is option B.

(As a quick check: since $1\ \text{V} = 1\ \text{J C}^{-1}$, rearranging gives $1\ \text{C} = 1\ \text{J V}^{-1}$.)

Key Takeaways

• Use definitions to convert units: $V = W/Q$ is a standard route.
• Rearranging a defining equation is a reliable way to identify equivalent derived units.
• Remember: $1\ \text{C} = 1\ \text{A}\,\text{s} = 1\ \text{J V}^{-1}$.

Common Mistakes

• Confusing $\text{A}\,\text{s}$ with $\text{A s}^{-1}$ (option A says ampere per second, which is not charge).
• Mixing up watts and joules: $1\ \text{W} = 1\ \text{J s}^{-1}$, so introducing W can add an extra time factor if handled carelessly.
• Treating $V = IR$ as the only definition of volt; it is fine, but here $V = W/Q$ is more direct.

Things to Be Careful About

• Read compound units carefully: “per second” means divide by seconds (power $\text{s}^{-1}$ appears), not multiply.
• Keep track of what is being defined: volts relate energy to charge, so rearrangement naturally gives charge in terms of joules and volts.
• In MCQs, choose the shortest consistent route: here, comparing to $V = W/Q$ avoids unnecessary substitutions with $P = VI$ or $W = Pt$.