Electrical Power

• The primary relationship for electrical power is the product of the potential difference across a component and the current flowing through it.

Fundamental Formula: $P = I \times V$

• In this equation, $P$ is power in Watts (W), $I$ is current in Amperes (A), and $V$ is potential difference in Volts (V).

• This relationship shows that for a constant voltage, increasing the current will linearly increase the power output of the device.

• By substituting Ohm's Law ($V = IR$) into the primary power equation, we can derive formulas that relate power directly to resistance.

• Current-Resistance Relationship: $P = I^2 R$. This is particularly useful for components in series where the current is constant.

• Voltage-Resistance Relationship: $P = \frac{V^2}{R}$. This is most effective for components in parallel where the potential difference is constant.

• These formulas demonstrate that power dissipation in a resistor is proportional to the square of the current or the square of the voltage.

• Energy ($E$) is the total amount of work done over a specific duration of time ($t$).

• The relationship between energy and power is defined by the product of power and the time interval of operation.

Energy Formula: $E = P \times t = I \times V \times t$

• To ensure the energy is calculated in Joules (J), the time must always be expressed in seconds (s).

• Alternatively, energy can be expressed in terms of charge ($Q$) and potential difference: $E = Q \times V$.

• It is critical to distinguish between the rate of use (Power) and the total amount used (Energy).

• In series circuits, the component with the highest resistance dissipates the most power because $P = I^2 R$ and $I$ is constant.

• In parallel circuits, the component with the lowest resistance dissipates the most power because $P = \frac{V^2}{R}$ and $V$ is constant.

• Unit Consistency: Always check that time is in seconds. If a problem provides time in minutes or hours, convert it immediately ($1 \text{ min} = 60 \text{ s}$).

• Formula Selection: Choose the power formula based on what remains constant. Use $I^2 R$ for series and $\frac{V^2}{R}$ for parallel to simplify calculations.

• Sanity Check: Remember that 'Watt' is 'Joule per second'. If you are asked for energy, your final answer should be in Joules; if asked for power, it should be in Watts.

• Proportionality: If the voltage across a fixed resistor doubles, the power does not just double—it quadruples because $P \propto V^2$.