(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600...

Irvin Dukes

Irvin Dukes

Answered

2021-12-31

(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. (b) Compute the reactance of a 2.50μ capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50μ capacitor?

Answer & Explanation

Alex Sheppard

Alex Sheppard

Expert

2022-01-01Added 36 answers

Step 1
Given
The inductance of the coil is L=0.45H.
Solution
(a) For ac source connected with a coil, the inductance reactance XL in the circuit is given by equation 31.12 in the form
XL=2πfL
This inductance reactance is related to the frequency f and the inductance L of the coil. Now, we want to get XL at f=60Hz and 600 Hz.
For f=60Hz:
XL=2πfL=2π(60Hz)(0.45H)=170Ω
For f=600Hz :
XL=2πfL=2π(600Hz)(0.45H)=1700Ω
Pademagk71

Pademagk71

Expert

2022-01-02Added 34 answers

Step 2
(b) The capacitance of the capacitor is C=2.5μF. The capacitive reactance XC in the circuit is given by equation 31.18 in the form
XC=12πfC
Now, we calcaute XC or 60 Hz and 600 Hz as next
XC(60)=12πfC=12π(60Hz)(2.5×106F)=1.06×103Ω
XC(600)=12πfC=12π(600Hz)(2.5×106F)=106Ω
Vasquez

Vasquez

Expert

2022-01-07Added 457 answers

Step 3
(c) In this part, the two reactance XCX and XLX are the same but at a specific frequency f. We are asked to determine the value of this frequency.
XC=XL
12πfC=2πfL
f=12πLC
Now plug the values for LL and CC into equation (3) to get f
=12πLC=12π(0.45H)(2.5×106F)=150Hz

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