Problem 31.50 At a frequency ? 1 the reactance of a certain capacitor equals tha

Question

Problem 31.50

At a frequency ?1 the reactance of a certain capacitor equals that of a certain inductor.

Part A

If the frequency is changed to ?2= 5 ?1, what is the ratio of the reactance of the inductor to that of the capacitor?

Part B

If the frequency is changed to ?3=?1/ 2, what is the ratio of the reactance of the inductor to that of the capacitor?

Problem 31.50 Part A If the frequency is changed to a 2 the capacitor? 5 wi, what is the ratio of the reactance of the inductor to that of At a frequency w1 the reactance of a certain capacitor equals that of a certain inductor. Submit My Answers Give Up Incorrect; Try Again; 9 attempts remaining Part B If the frequency is changed to a 3-w1 / 2, what is the ratio of the reactance of the inductor to that of the capacitor? Xc Submit My Answers Give Up

Explanation / Answer

frequency w1

inductive reactance is XL

capacitive reactance is XC

===>XC=XL

1/w1*C=W1*L

===> w1^2=1/(L*C)   -------(1)

A)

if W2=5*W1

==>

XL/XC=(W2*L)/(1/w2*C)

=w2^2*(LC)

=w2^2*(1/w1^2) <---- ( from(1) )

==>

XL/XC=(w2/w1)^2 ---(2)

XL/XC=(5W1/W1)^2

XL/XC=25

===> XL/Xc=25

B)

if w3=w1/2

from equation (2)

XL/XC=(w3/w1)^2

XL/XC=(w1/2*W1)^2

XL/XC=1/4

===> XL/Xc=0.25

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