Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 84

A charging \(R C\) circuit controls the intermittent windshield wipers in a car. The emf is \(12.0 \mathrm{V}\). The wipers are triggered when the voltage across the 125 - \(\mu\) F capacitor reaches \(10.0 \mathrm{V} ;\) then the capacitor is quickly discharged (through a much smaller resistor) and the cycle repeats. What resistance should be used in the charging circuit if the wipers are to operate once every \(1.80 \mathrm{s} ?\)

Short Answer

Expert verified
Answer: The required resistance for the charging circuit is approximately \(1143.72 \, \Omega\).

Step by step solution

01

Identify the variables in the problem

The given values are: Voltage when the capacitor in the charging circuit is triggered (V_c): 10.0V Initial voltage across the capacitor (V_0): 12.0V Capacity of the capacitor (C): 125µF Time it takes for the wiper to operate (t): 1.80s Resistance (R): Unknown
02

Re-write the formula in terms of R

We are trying to find R, so we need to rewrite the equation in terms of R. Since we have: \(V_c(t) = V_0(1 - e^{-t/(RC)})\) We can divide both sides by V_0 to isolate the exponential part: \(\frac{V_c}{V_0} = 1 - e^{-t/(RC)}\) We can now make it easier to solve for R: \(e^{-t/(RC)} = 1 - \frac{V_c}{V_0}\) \(-t/(RC) = \ln(1 - \frac{V_c}{V_0})\) \(R = -t / (C \ln(1 - \frac{V_c}{V_0}))\)
03

Plug in the values and solve for R

Now, we can plug in the values to find R: \(R = -1.80 / (125 \times 10^{-6} \ln(1 - \frac{10.0}{12.0}))\) Calculate the value of R: \(R \approx 1143.72 \, \Omega\) Therefore, a resistance of approximately \(1143.72 \, \Omega\) should be used in the charging circuit for the windshield wipers to operate once every 1.80 seconds.

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

During a "brownout," which occurs when the power companies cannot keep up with high demand, the voltage of the household circuits drops below its normal $120 \mathrm{V} .\( (a) If the voltage drops to \)108 \mathrm{V},$ what would be the power consumed by a "100-W" light-bulb (that is, a light-bulb that consumes \(100.0 \mathrm{W}\) when connected to \(120 \mathrm{V}\) )? Ignore (for now) changes in the resistance of the light-bulb filament. (b) More realistically, the light-bulb filament will not be as hot as usual during the brownout. Does this make the power drop more or less than that you calculated in part (a)? Explain.
A Vespa scooter and a Toyota automobile might both use a \(12-\mathrm{V}\) battery, but the two batteries are of different sizes and can pump different amounts of charge. Suppose the scooter battery can pump 4.0 kC of charge and the automobile battery can pump \(30.0 \mathrm{kC}\) of charge. How much energy can each battery deliver, assuming the batteries are ideal?
A battery has a \(6.00-\mathrm{V}\) emf and an internal resistance of $0.600 \Omega$. (a) What is the voltage across its terminals when the current drawn from the battery is \(1.20 \mathrm{A} ?\) (b) What is the power supplied by the battery?
A solar cell provides an emf of \(0.45 \mathrm{V}\). (a) If the cell supplies a constant current of \(18.0 \mathrm{mA}\) for \(9.0 \mathrm{h},\) how much electric energy does it supply? (b) What is the power-the rate at which it supplies electric energy?
A string of 25 decorative lights has bulbs rated at \(9.0 \mathrm{W}\) and the bulbs are connected in parallel. The string is connected to a \(120-\mathrm{V}\) power supply. (a) What is the resistance of each of these lights? (b) What is the current through each bulb? (c) What is the total current coming from the power supply? (d) The string of bulbs has a fuse that will blow if the current is greater than 2.0 A. How many of the bulbs can you replace with 10.4-W bulbs without blowing the fuse?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Fluids

Read Explanation

Atoms and Radioactivity

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Energy Physics

Read Explanation

Quantum Physics

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