How does voltage affect the brightness of a lightbulb in a circuit?

Power (P) = Voltage (V) × Current (I)

When a lightbulb is connected to a circuit, it has a certain resistance (R) value, which represents its opposition to the flow of electric current. According to Ohm's Law, the current flowing through the lightbulb can be calculated as:

Current (I) = Voltage (V) / Resistance (R)

If the resistance of the lightbulb remains constant, we can rearrange the equations to see how brightness changes with voltage:

Power (P) = Voltage (V) × Current (I)

Power (P) = Voltage (V) × (Voltage (V) / Resistance (R))

Power (P) = (Voltage (V))^2 / Resistance (R)

From this equation, it is evident that the power (brightness) of the lightbulb is directly proportional to the square of the voltage across it. This means that if you increase the voltage supplied to the lightbulb, its brightness will increase, and if you decrease the voltage, its brightness will decrease.

It's important to note that while the brightness increases with voltage, you must also be cautious not to exceed the recommended voltage for the lightbulb, as excessive voltage can cause the bulb to burn out or even become a safety hazard. Always use the rated voltage specified for the lightbulb by the manufacturer to ensure safe and optimal operation.