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

The heating element of an electric dryer is rated at 4.1 kW when connected to a 240-V line. (a) What is the current in the heating element? Is 12-gauge wire large enough to supply this current? (b) What is the resistance of the dryer’s heating element at its operating temperature? (c) At 11 cents per kWh, how much does it cost per hour to operate the dryer?

The potential difference across the terminals of a battery is 8.40 V when there is a current of 1.50 A in the battery from the negative to the positive terminal. When the current is 3.50 A in the reverse direction, the potential difference becomes10.20 V . (a) What is the internal resistance of the battery? (b) What is the emf of the battery?

Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500V and produce currents of 80mA(or even larger). A typical pulse lasts for 10ms. What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?

The text states that good thermal conductors are also good electrical conductors. If so, why don’t the cords used to connect toasters, irons, and similar heat-producing appliances get hot by conduction of heat from the heating element?

A rule of thumb used to determine the internal resistance of a source is that it is the open circuit voltage divide by the short circuit current. Is this correct? Why or why not?

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