(a) What is the resistance of the heater element in a 1500-W hair dryer that plugs into a 120-V

step 1 Using the formula power equals whisper over r, we find that R equals v square over p equals 120

(a) What is the resistance of the heater element in a 1500-W...

(a) What is the resistance of the heater element in a $1500-\mathrm{W}$ hair dryer that plugs into a $120-\mathrm{V}$ outlet? (b) What is the current through the hair dryer when it is turned on? (c) At a cost of $\$ 0.10$ per kW .h, how much does it cost to run the hair dryer for 5.00 min? (d) If you were to take the hair dryer to Europe where the voltage is $240 \mathrm{V},$ how much power would your hair dryer be using in the brief time before it is ruined? (e) What current would be flowing through the hair dryer during this time?

(a) What is the resistance of the heater element in a $1500-\mathrm{W}$ hair dryer that plugs into a $120-\mathrm{V}$ outlet?
(b) What is the current through the hair dryer when it is turned on? (c) At a cost of $\$ 0.10$ per kW .h, how much does it cost to run the hair dryer for 5.00 min? (d) If you were to take the hair dryer to Europe where the voltage is $240 \mathrm{V},$ how much power would your hair dryer be using in the brief time before it is ruined? (e) What current would be flowing through the hair dryer during this time?

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits stating that the voltage across a resistor is directly proportional to the current flowing through it and the resistance. This relationship, often expressed as V = I × R, is crucial for understanding and analyzing how electrical circuits behave.

Power in Resistive Circuits

In electrical circuits, the power dissipated by a resistor can be calculated using formulas such as P = V²/R, P = I² × R, or P = V × I. These formulas help determine how much electrical energy is converted into heat, which is fundamental in designing and analyzing devices.

Energy Consumption and Cost Calculation

Energy consumption in electrical devices is determined by the product of power and the duration of operation, with power measured in watts and time in hours, resulting in energy quantified in kilowatt-hours (kWh). This measure is essential when calculating operating costs based on energy usage and pricing per unit of energy.

Effects of Voltage Variation on Resistive Loads

Changing the voltage applied to a resistive load has a significant impact on the power consumed because of the quadratic relationship in the formula P = V²/R. This means that even small increases in voltage can lead to large increases in power consumption, which is important when considering device ratings and safety.

Unit Conversion in Electrical Calculations

Accurate unit conversion is critical in electrical calculations to ensure consistency and correctness. This involves converting units such as minutes to hours when calculating energy consumption, or watts to kilowatts when relating power to energy billing, ensuring proper alignment in all calculations.

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