Ch 32: AC Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 32: AC Circuits

Problem 34

Chapter 32, Problem 34

The heating element of a toaster dissipates 1500 W when connected to a 120 V/60 Hz power line. What is its resistance?

Verified step by step guidance

Start by recalling the formula for electrical power dissipation in terms of voltage and resistance:

P = V^{2} / R

, where

P

is the power,

V

is the voltage, and

R

is the resistance.

Rearrange the formula to solve for resistance

R

R = V^{2} / P

Substitute the given values into the formula:

V = 120

volts and

P = 1500

watts.

Square the voltage:

V^{2} = 120^2

Divide the squared voltage by the power to find the resistance:

R = 120^2 / 1500

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = I * R. This relationship is fundamental in electrical circuits and helps in calculating resistance when voltage and current are known.

Power in Electrical Circuits

The power (P) dissipated in an electrical circuit is the rate at which energy is used or converted and is calculated using the formula P = V * I, where V is voltage and I is current. In the context of resistive devices like a toaster, power can also be expressed as P = I^2 * R or P = V^2 / R, allowing for the calculation of resistance when power and voltage are known.

Resistance

Resistance (R) is a measure of the opposition to the flow of electric current in a conductor. It is measured in ohms (Ω) and depends on the material, length, and cross-sectional area of the conductor. In the context of the toaster, calculating resistance is essential to understand how efficiently it converts electrical energy into heat, which is crucial for its operation.

Recommended video:

Guided course

05:25

Resistivity & Resistors in Circuits

Related Practice

Textbook Question

For the circuit of FIGURE EX32.32, What is the resonance frequency, in both rad/s and Hz?

views

Textbook Question

For the circuit of FIGURE EX32.32, Find V_R and V_L at resonance.

views

Textbook Question

A resistor dissipates 2.0 W when the rms voltage of the emf is 10.0 V. At what rms voltage will the resistor dissipate 10.0 W?

views

Textbook Question

For the circuit of FIGURE EX32.33, What is the resonance frequency, in both rad/s and Hz?

views

Textbook Question

A series RLC circuit with a 100 Ω resistor dissipates 80 W when attached to a 120 V/60 Hz power line. What is the power factor?

views

Textbook Question

The motor of an electric drill draws a 3.5 A rms current at the power-line voltage of 120 V rms. What is the motor's power if the current lags the voltage by 20°?

views