The wattage rating of a lightbulb is the power it consumes...

The wattage rating of a lightbulb is the power it consumes when it is connected across a $120 \mathrm{~V}$ potential difference. For example, a $60 \mathrm{~W}$ lightbulb consumes $60.0 \mathrm{~W}$ of electric power only when it is connected across a $120 \mathrm{~V}$ potential difference. (a) What is the resistance of a $60 \mathrm{~W}$ lightbulb? (b) Without doing any calculations, would you expect a $100 \mathrm{~W}$ bulb to have more or less resistance than a $60 \mathrm{~W}$ bulb? Calculate and find out.

The wattage rating of a lightbulb is the power it consumes when it is connected across a $120 \mathrm{~V}$ potential difference. For example, a $60 \mathrm{~W}$ lightbulb consumes $60.0 \mathrm{~W}$ of electric power only when it is connected across a $120 \mathrm{~V}$ potential difference.
(a) What is the resistance of a $60 \mathrm{~W}$ lightbulb? (b) Without doing any calculations, would you expect a $100 \mathrm{~W}$ bulb to have more or less resistance than a $60 \mathrm{~W}$ bulb? Calculate and find out.

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electricity that states the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It provides the basis for understanding how voltage, current, and resistance interact in a circuit.

Electric Power Consumption

Electric power describes the rate at which electrical energy is used or converted into another form, such as heat or light. It is commonly expressed in watts (W) and can be related to voltage and resistance by the formula P = V²/R, which is crucial for analyzing how devices consume power under specific voltage conditions.

Relationship Between Power and Resistance

In circuits with a constant applied voltage, the power consumed by an electrical device is inversely proportional to its resistance. This means that devices with lower resistance will draw more power, while those with higher resistance will draw less power, illustrating how design specifications such as wattage ratings can indicate the internal resistance of a device.

Constant Voltage Conditions

Operating under constant voltage conditions means that the voltage applied to the device remains fixed. This concept is important because it allows for a direct analysis of how changes in resistance affect power consumption, facilitating the understanding of device ratings and comparisons under standardized supply conditions.

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