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Chapter 32: Q. 31 (page 925)

At what frequency f do a 1.0渭Fcapacitor and a 1.0渭Hinductor have the same reactance? What is the value of the reactance at this frequency?

Short Answer

Expert verified

Frequency ; f =159kHz

Reactance ; X=9.98脳10-4惟

Step by step solution

01

:Given Information

We have been given that

Capacitance of capacitor,C=1.0渭F=10-6F

Inductance of inductor,L=1.0渭H=10-6H

We need to find out the frequency at which the reactance of inductor and capacitor is same and the reactance at that frequency.

02

Explanation 

Given , C=1渭Fand L=1渭H

As we know Capacitive Reactance ;

XC=12蟺fC.....(1)

where f is frequency ;

C is capacitance;

XCis capacitive reactance

Also,

Inductive Reactance ; XL=2蟺fL .......(2)

where f is frequency ;

L is inductance

Since, both Reactance are same i.eXL=XC

鈬�2蟺fL=12蟺fC鈬�f=12蟺CL=12(3.14)(1脳10-6F)(1脳10-6H)鈬�f=159kHz

Now reactance at frequency ,f

XL=XC=2蟺fL=2(3.14)(159脳103Hz)(1脳10-6H)=9.98脳10-4惟

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