Final answer:
The power dissipated in a circuit element is given by the equation P = V² / R, indicating that power increases with the square of the voltage and decreases with higher resistance.
Step-by-step explanation:
The equation for the power (P) dissipated in a circuit element in terms of voltage (V) and resistance (R) is P = V² / R. This equation suggests that the lower the resistance for a given voltage, the higher the power that is dissipated. It also shows that the power dissipation increases dramatically with an increase in voltage because the voltage term is squared in the equation.
For example, if the voltage across a device is doubled, the power dissipation increases by a factor of four, assuming the resistance remains constant. This can lead to significant consequences, such as a light bulb burning out if subject to a higher voltage than it is rated for.
These insights are obtained by combining Ohm's law (V = IR) with the power equation (P = IV), which provides us with different expressions for electric power, including the one relating voltage and resistance: P = V² / R.