Suppose a voltage surge produces 140 V for a moment. By what percentage does the power output of

step 1 Here the power formula can be written as p is equal to b square upon r. Therefore, the power is

Suppose a voltage surge produces 140 V for a moment. By what...

Suppose a voltage surge produces 140 $\mathrm{V}$ for a moment. By what percentage does the power output of a $120-\mathrm{V}, 100-\mathrm{W}$ lightbulb increase? Assume its resistance does not change.

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Key Concepts

Percentage Increase Calculation

Calculating the percentage increase involves determining the difference between the new and original power levels, divided by the original power level, and then multiplying by 100. This method quantifies the relative change and provides a clear indication of how much the power output has increased as a result of the voltage change.

Relationship between Voltage and Power

The direct dependency of power on the square of the voltage means that even a modest increase in voltage can produce a considerably larger increase in power. This concept is critical in understanding why devices may draw significantly more power during voltage surges.

Electrical Power in Resistive Loads

In circuits with a resistor, the power dissipated is given by P = V²/R. This formula shows that if the resistance is constant, any change in the applied voltage will change the power output by the square of the voltage ratio, demonstrating a quadratic relationship.

Constant Resistance Assumption

Assuming that the resistance remains constant simplifies the analysis by ensuring that the only variable affecting the power output is the voltage. This assumption is valid in many practical cases where the object's temperature and material properties do not vary significantly with the applied voltage over short durations.

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