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

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