You buy a light bulb in the U. S. labeled 75 watts. Since you bought it in the U. S., the power rating assumes that the potential difference across the light bulb will be 120 volts. Instead, you provide it with a potential difference of 220 volts (the potential difference provided by wall outlets in most European countries). Will the light bulb dissipate 75 watts of power?

P₂ = 252 W

Explanation:

The electrical power is

P = V I

The potential difference is

V = I R

I = V / R

Let's replace

P = V² / R

Let's use the given values to calculate the resistance of the bulb

R = V² / P

R = 120²/75

R = 192 ohm

This resistance value does not depend on the applied voltage, so it is constant

Let's calculate the power in Europe

P₂ = V₂² / R

P₂ = 220²/192

P₂ = 252 W

the bulb dissipates much more power

The light bulb will not dissipate 75 Watts of power when provided with 220 volts

Explanation:

The resistance of the bulb does not change

Let P = Power

V = Voltage

R = Resistance

P = V²/R

When Power = 75 Watts and Voltage = 120 volts

75 = (120) ²/R

R = (120) ²/75

R = 192 ohms

Since the resistance of the bulb is constant

When V = 220 volts

P = V²/R

P = 220²/192

P = 252.08 W