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Chapter 32: Q. 58 (page 926)

Show that the power factor of a series RLC circuit iscos蠒=RZ

Short Answer

Expert verified

We have prove that,

Power factor, cos蠒=RZ

Required proof is given below.

Step by step solution

01

Given information

We need to find out that,

Power factor is, cos蠒=RZ

02

Simplify

We know that,

Power dissipated by LCR circuit is, P=I2Zcos蠒

Here, Iis current in LCR circuit

And Zis impedance

And cos蠒is power factor

Also, we know that power, P=VI

Where Vis voltage across resistor as in series voltage remain same across resistor, inductor and capacitor

Therefore, V=IR

Where Ris resistance

Therefore,

P=I2Zcos蠒=VII2Zcos蠒=IRII2Zcos蠒=I2Rcos蠒=RZ

Hence we get the require expression i.e.cos蠒=RZ

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Most popular questions from this chapter

Use a phasor diagram to analyze the RL circuit of FIGURE P32.49. In particular,

a. Find expressions for I,VRandVL.

b. What is VR in the limits 蝇鈫�0and 蝇鈫�鈭�?

c. If the output is taken from the resistor, is this a low-pass or a high-pass filter? Explain.

d. Find an expression for the crossover frequency 蝇C.

a. Evaluate VR in figure at emf frequencies100,300,1000,3000,10000Hz

b. Graph VRversus frequency. Draw a smooth curve through your five points.

For what absolute value of the phase angle does a source deliver 75%of the maximum possible power to an RLC circuit?

For an RC filter circuit, show thatVR=VC=蔚02at蝇=蝇c.

A television channel is assigned the frequency range from 54mHZto 60mHZ. A series RLC tuning circuit in a TV receiver resonates in the middle of this frequency range. The circuit uses a 16pFcapacitor.

a. What is the value of the inductor?

b. In order to function properly, the current throughout the frequency range must be at least 50% of the current at the resonance frequency. What is the minimum possible value of the circuit鈥檚 resistance?
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