Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

In the circuit shown in Fig. E26.41, both capacitors are initially charged to 45.0 V. (a) How long after closing the switch S will the potential across each capacitor be reduced to 10.0 V, and (b) what will be the current at that time?

Short Answer

Expert verified

Answer:

(a) After4.21×10-3s closing the switch the potential across each capacitor is reduced to .

(b) The at that time will be0.125A

Step by step solution

01

Concept

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals. The effect of a capacitor is known as capacitance.

02

Adding capacitance and resistance

From the above circuit we can see thatC1=15.0μF,C2=20.μF, and R1=30.0Ω,R2=50.0Ωthe switch is closed at the time .

Now, since both the capacitors are initially charged to we are required to find the equivalent capacitance and resistance to reduce the circuit to a simple circuit. Now we know that the capacitance adds in parallel and the resistance adds in series, hence we can write the thing in:

Req=R1+R2Ceq=C1+C2

Now let us substitute the values to get:

Req=(30.0+50.0)Ω=80.0ΩCeq=(15.0+20.0)μF=35.0μF

03

Calculating the time taken

While discharging the capacitor, the charge on the capacitor is given by:

Q=Q0e-tτ

Where τ=ReqCeqis the time constant, Q=CVCbut and Q=CVC0, we can write:

VC=VC0e-tτ

Now, we need to find how long after the closing of the switch S will the potential defense across each of the capacitors reduced to , therefore we need to solve for :

t=-τlnVCVC0

Now, putting the values we get:

t=-(2.80×10-3s)ln10.0V45.0V=4.21×10-3s

Therefore, the time taken is:

04

Calculating current

The current at a time is defined by

I=VC0Req=VC0Reqe-tτ

Plugging in the values we get:

I=VC0Reqe-tτ=45.080.0e-4.21×10-3s2.80×10-3s=0.125A

Therefore, the current is 0.125 A

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.

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

A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of12Athrough the body at25Vfor a very short time, usually3.0msabout . (a) What power does the defibrillator deliver to the body, and (b) how much energy is transferred ?

A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80

min. Silver containsfree electrons per cubic meter. (a) What is the

current in the wire? (b) What is the magnitude of thedrift velocity of the

electrons in the wire?

An electrical conductor designed to carry large currents has a circular cross section 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is 0.104Ω. (a) What is the resistivity of the material? (b) If the electric-field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5×1028free electrons per cubic meter, find the average drift speed under the conditions of part (b).

A particle with charge-5.60nCis moving in a uniform magnetic fieldrole="math" localid="1655717557369" B=-(1.25T)k^

The magnetic force on the particle is measured to berole="math" localid="1655717706597" F=-(3.40×10-7N)i^-(7.40×10-7N)j^ (a) Calculate all the components of the velocity of the particle that you can from this information. (b) Are there
components of the velocity that are not determined by the measurement of the force? Explain. (c) Calculate the scalar productv֏F. What is the angle between velocity and force?

Copper has 8.5×1022free electrons per cubic meter. A 71.0-cm

length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of

current. (a) How much time does it take for an electron to travel the length

of the wire? (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm)

of the same length that carries the same current. (c) Generally speaking,

how does changing the diameter of a wire that carries a given amount of

current affect the drift velocity of the electrons in the wire?

See all solutions

Recommended explanations on Physics Textbooks

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