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 an L-R-C series circuit, the components have the following values: L = 20.0 mH, C = 140 nF, and R = 350Ω. The generator has an rms voltage of 120V and a frequency of 1.25 kHz. Determine (a) the power supplied by the generator and (b) the power dissipated in the resistor.

Short Answer

Expert verified

The power supplied by the generator is 7.32 W and the power dissipated by the generator is 7.32 W.

Step by step solution

01

Step-1: Formula of power supplied and power dissipated  

ϕis the phase difference between voltage and current.

ϕistan-1(wL-1ωCR)whereϕ is the phase difference between voltage and current,ω is the angular frequency of voltage supply, L is the value of inductance of the inductor, C is the capacitance, R is the resistance

Irmsrepresents the d.c. current/voltage that dissipates the same amount of power as the average power dissipated by the alternating current/voltage.

Irms=VrmsZ

Pavgis the average power dissipated by the circuit.

Pavg=VrmsIrmscosϕ=(Irms)2R

VrmsandIrms are the rms voltage and current respectively.

Z is defined as the impedance of the circuit which is the effective resistance of an electric circuit or component to alternating current, arising from the combined effects of ohmic resistance and reactance.

Z=R2+(XL-XCC)2, where Z is the impedance

02

Step-2: Calculations for power supplied by the generator

ϕ=tan-1(157Ω-909Ω350Ω)-65.04°

z=3502+157-9092Ω=829.8Ω

Irms=120V829.8Ω=0.145A

Finally,Pavg=(120.V)(0145A)cos(-65.04)=7.32W

Therefore the value of the power supplied by the generator is 7.32W

03

Step-3: Calculations for power dissipated by the resistor

Pavg=(0.145A)2(350Ω)=7.32W

Therefore the value of the power supplied by the generator is 7.32W and the value of the power dissipated by the generator is 7.32W.

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

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