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

step 1 Solving part A of this problem, so we know that p is equal to b square by r. So I can write the

(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 $\mathrm{kW} \cdot \mathrm{h},$ 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 $\mathrm{kW} \cdot \mathrm{h},$ 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

Voltage Effects on Device Operation

Voltage, the electrical potential difference, significantly influences the behavior of a device with a given resistance. Changes in voltage can alter both the power consumption and the current drawn by the device, potentially affecting performance and safety when operating under voltages different from the device's design specifications.

Energy Consumption and Cost Calculation

Energy consumption refers to the total amount of electrical energy used by a device over time, often measured in kilowatt-hours (kWh). It can be calculated by multiplying the device's power rating by the time it operates. This concept is directly tied to cost calculations when energy prices are given per kilowatt-hour.

Electrical Power

Electrical power is the rate at which energy is transferred or used in an electrical circuit. It is calculated using relationships such as P = VI, P = I²R, or P = V²/R. Understanding power helps in determining how much energy a device uses or how it operates under different voltage or resistance conditions.

Electrical Resistance

Electrical resistance measures how much a material opposes the flow of electric current. It is an intrinsic property of components and is measured in ohms (?). Resistance plays a fundamental role in relating voltage and current in a circuit through Ohm's Law.

Ohm's Law

Ohm's Law establishes the relationship among voltage, current, and resistance in a circuit, expressed as V = IR. This fundamental principle is used to determine one of these quantities when the other two are known, and is essential for analyzing and designing electrical circuits.

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