recall and use V = W / Q

Potential Difference and Power

Objective

Recall and use the relationship

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

where V is the potential difference (volts), W is the work done or energy transferred (joules), and Q is the charge moved (coulombs).

Key Concepts

• Potential Difference (Voltage) – the energy per unit charge required to move a charge between two points.
• Electric Power – the rate at which electrical energy is transferred or converted.
• Current (I) – the flow of charge per unit time, measured in amperes (A).

Mathematical Relationships

The fundamental definitions lead to several useful formulas:

• Potential difference: $V = \dfrac{W}{Q}$
• Current: $I = \dfrac{Q}{t}$
• Power: $P = \dfrac{W}{t}$

Combining the above gives the commonly used power–voltage–current relationship:

$$P = V I$$

Substituting $I = \dfrac{Q}{t}$ into $P = V I$ also yields:

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

Thus power can be expressed in three equivalent forms:

$$P = V I = \frac{W}{t} = \frac{V Q}{t}$$

Units and Symbols

Quantity	Symbol	SI Unit	Unit Symbol
Potential Difference (Voltage)	V	joule per coulomb	V
Work / Energy	W	joule	J
Charge	Q	coulomb	C
Current	I	coulomb per second	A
Power	P	joule per second	W
Time	t	second	s

Worked Example

1. A heater uses a voltage of $240\ \text{V}$ and draws a current of $10\ \text{A}$. Calculate the power output.
2. Apply $P = V I$: $$P = 240\ \text{V} \times 10\ \text{A} = 2400\ \text{W}$$
3. Interpretation: The heater converts electrical energy to heat at a rate of $2.4\ \text{kW}$.

Common Mistakes to Avoid

• Confusing $V = \dfrac{W}{Q}$ with $V = \dfrac{Q}{W}$. The numerator must be energy (or work), the denominator charge.
• Using the symbol $V$ for both voltage and speed in the same context; keep symbols distinct.
• Omitting the time factor when converting between energy (J) and power (W). Remember $1\ \text{W} = 1\ \text{J s}^{-1}$.
• Mixing up the units of charge (C) and current (A). Current is charge per unit time.

Suggested Diagram