recall and use V = W / Q

Potential Difference and Power ⚡️

What is Potential Difference?

Potential difference (voltage) is the energy per unit charge that moves between two points in an electric field. Think of it as the “pressure” that pushes electrons through a wire, just like water pressure pushes water through a pipe.

The Work–Charge Relationship

When a charge $Q$ moves through a potential difference $V$, the work done (energy transferred) is

$$W = V \times Q$$

Rearranging gives the formula you need to remember:

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

Power – How Fast Energy is Used

Power is the rate at which energy is transferred or used. In electricity, power $P$ is the work done per unit time.

$$P = \frac{W}{t}$$

Because $W = VQ$, we can also write power in terms of voltage and current ($I = Q/t$):

$$P = V \times I$$

Quick Reference Table 📚

Example Problem 🧮

1. A 2‑C charge moves through a potential difference of 12 V. What is the work done?
2. A lightbulb uses 60 W of power and operates at 12 V. What is the current flowing through it?

Answers:

• Work: $W = V \times Q = 12\,\text{V} \times 2\,\text{C} = 24\,\text{J}$.
• Current: $I = \dfrac{P}{V} = \dfrac{60\,\text{W}}{12\,\text{V}} = 5\,\text{A}$.

Key Take‑aways 🔑

• Potential difference is the “push” that moves charge.
• Use $V = W/Q$ to find voltage when you know work and charge.
• Power tells you how fast energy is used: $P = V I$ is the most common form.
• Always check units: V (volts), J (joules), C (coulombs), A (amps), W (watts).