The relationship between voltage and power across a resistive element is described by Ohm's Law, which states that power (P) is equal to the product of voltage (V) and current (I), or P = VI. Therefore, if the voltage is doubled, the power will also double, assuming the resistance of the element remains constant.
In the case of the lightbulb, if it is rated at 100W when 140V is used, the current flowing through it can be calculated using Ohm's Law as I = P/V = 100/140 = 0.71A. If the voltage is doubled to 280V, the current will also double to 1.42A, resulting in a power of 200W (P = VI = 280 x 1.42 = 200W).
It is important to note that this relationship only holds true for resistive elements, as the power dissipated in other types of elements (such as capacitors or inductors) can be affected by factors such as frequency and phase difference between voltage and current.
Additionally, it is important to consider the limitations of the lightbulb and not exceed its rated voltage, as this can lead to overheating and potentially cause the bulb to explode. In cases where higher power is needed, it is recommended to use a higher wattage bulb rather than increasing the voltage.