Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 30: Problem 61

What are the maximum values of (a) current and (b) voltage when an incandescent 60 -W light bulb (at \(110 \mathrm{~V})\) is connected to a wall plug labeled \(110 \mathrm{~V} ?\)

Short Answer

Expert verified
Answer: The maximum current for the light bulb is calculated using the formula \(I_\text{max} = \frac{110 \mathrm{~V}}{R}\), where R is the resistance of the light bulb. The maximum voltage for the light bulb is given and is 110 V.

Step by step solution

01

Calculate the resistance of the light bulb

First, we need to find the resistance of the light bulb. We can do this using the power formula: \(P = V^2/R\), where P is the power in watts, V is the voltage in volts, and R is the resistance in ohms. Rearranging the formula for R gives: \(R = \frac{V^2}{P}\). Given the power of the bulb (P) to be 60 W and the voltage (V) to be 110 V, we can plug in these values and calculate the resistance of the light bulb: \(R = \frac{(110 \mathrm{~V})^2}{60 \mathrm{~W}}\)
02

Calculate the maximum current

Now that we have the resistance, we can use Ohm's law to calculate the maximum current. Ohm's law states: \(I = \frac{V}{R}\), where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms. Using the voltage given for the wall plug, 110 V, and the calculated resistance, we can find the maximum current: \(I_\text{max} = \frac{110 \mathrm{~V}}{R}\)
03

Calculate the maximum voltage

The maximum voltage is already given by the problem as 110 V. This is because the voltage across the light bulb is determined by the voltage of the wall plug to which it is connected. So, \(V_\text{max} = 110 \mathrm{~V}\)
04

Final answers

Calculating the values from the previous steps, we find the maximum current and voltage for the light bulb: (a) Maximum Current: \(I_\text{max} = \frac{110 \mathrm{~V}}{R}\) (b) Maximum Voltage: \(V_\text{max} = 110 \mathrm{~V}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Solved Problem 30.1 , the voltage supplied by the source of time-varying emf is \(33.0 \mathrm{~V}\), the voltage across the resistor is \(V_{R}=I R=13.1 \mathrm{~V}\), and the voltage across the inductor is \(V_{L}=I X_{L}=30.3 \mathrm{~V}\). Does this circuit obey Kirchhoff's rules?

What is the impedance of a series RLC circuit when the frequency of time- varying emf is set to the resonant frequency of the circuit?

A vacuum cleaner motor can be viewed as an inductor with an inductance of \(100 . \mathrm{mH} .\) For a \(60.0-\mathrm{Hz} \mathrm{AC}\) voltage, \(V_{\mathrm{rms}}=115 \mathrm{~V}\), what capacitance must be in series with the motor to maximize the power output of the vacuum cleaner?

An inductor with inductance \(L=47.0 \mathrm{mH}\) is connected to an AC power source having a peak value of \(12.0 \mathrm{~V}\) and \(f=1000 . \mathrm{Hz} .\) Find the reactance of the inductor and the maximum current in the circuit.

An AC power source with \(V_{\mathrm{m}}=220 \mathrm{~V}\) and \(f=60.0 \mathrm{~Hz}\) is connected in a series RLC circuit. The resistance, \(R\), inductance, \(L\), and capacitance, \(C\), of this circuit are, respectively, \(50.0 \Omega, 0.200 \mathrm{H},\) and \(0.040 \mathrm{mF}\). Find each of the following quantities: a) the inductive reactance b) the capacitive reactance c) the impedance of the circuit d) the maximum current through the circuit e) the maximum potential difference across each circuit element
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Measurements

Read Explanation

Famous Physicists

Read Explanation

Fluids

Read Explanation

Radiation

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free