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

For the circuit shown in FIGURE P28.60, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

Short Answer

Expert verified

The result is

R(Ω)
I(A)
V(V)
3
2
6
4
1.5
6
16
0.375
6
48
0.125
6

Step by step solution

01

Given Information 

We have to find the current through and the potential difference across each resistor.

02

Simplify 

The circuit can be simplified as shown in figure. in case if resistors are connected at both ends of two points then it is called resistors connected in parallel. This is obvious when the resistors are aligned side by side. The potential difference across the resistors is the same in parallel connection. Equation shows the equivalent resistance for the parallel connection in the form

1Req=1R1+1R2+....+1RN(1)

4Ω,48Ωand16Ω, these three resistors are in parallel, so use equation (1)to get their combination by

1R1,eq=14Ω+116Ω+148Ω1R1,eq=14Ω+116Ω+148Ω-1R1,eq=3Ω

The above combination is in the series with resistor 3Ω, so the equivalent resistance of the circuit is

Req=R1,eq+3Ω=3Ω+3Ω=6Ω

Also, the current is same for resistors in series, so the current through both resistors and the combination is calculated by using Ohm's law

I3=εReq=12V6Ω=2A

After using Ohm's law to get the voltage across resisors 3Ωby

localid="1649086636375" V=I3R3=(2A)(3Ω)=6V

localid="1649086640807" 4Ω,48Ωand16Ωresistors have the same voltage and their combination current is the same for I3, Using Ohm's law to get the voltage across each of the by

localid="1649086645233" V4=V48=V16=I3Req=(2A)(3Ω)=6V

03

Simplify 

Also we have to use Ohm's law to get current through 4Ω,48Ωand16Ωby

I4=V4R4=6V16Ω=1.5A

and

I16=V16R16=6V16Ω=0.375A

and

I16=V48R48=6V16Ω=0.125A

The results are in the next table

R(Ω)
I(A)
V(V)
3
2
6
4
1.5
6
16
0.375
6
48
0.125
6

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

How much current flows through the bottom wire in figureP28.66, and in which direction ?

The circuit of FIGURE Q28.4 has two resistors, with R1>R2. Which of the two resistors dissipates the larger amount of power? Explain.

An oscillator circuit is important to many applications. A simple oscillator circuit can be built by adding a neon gas tube to an RC circuit, as shown in figureCP28.83. Gas is normally a good insulator, and the resistance of the gas tube is essentially infinite when the light is off. This allows the capacitor to charge. When the capacitor voltage reaches a value Von, the electric field inside the tube becomes strong enough to ionize the neon gas. Visually, the tube lights with an orange glow. Electrically, the ionization of the gas provides a very-low-resistance path through the tube. The capacitor very rapidly (we can think of it as instantaneously) discharges through the tube and the capacitor voltage drops. When the capacitor voltage has dropped to a value Voff, the electric field inside the tube becomes too weak to sustain the ionization and the neon light turns off. The capacitor then starts to charge again. The capacitor voltage oscillates between Voff, when it starts charging, and Von, when the light comes on to discharge it.

a. Show that the oscillation period is

T=RCinε-Voffε-Von

b. A neon gas tube has Von=80VandVoff=20V. What resistor value should you choose to go with a 10μfcapacitor and a 90Vbattery to make a 10Hzoscillator?

What is the equivalent resistance between points a and b in FIGURE P28.45?

A refrigerator has a 1000Wcompressor, but the compressor runs only 20%of the time.

a. If electricity costs\(0.10/kWh, what is the monthly (30 day) cost of running the refrigerator?

b. A more energy-efficient refrigerator with an 800W compressor costs\)100 more. If you buy the more expensive refrigerator, how many months will it take to recover your additional cost?

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