(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 2.50−μ capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50−μ capacitor?

Question

Alex Sheppard · Accepted Answer

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 · Accepted Answer

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)(2.5×10−6F)=1.06×103Ω  XC(600)=12πfC=12π(600Hz)(2.5×10−6F)=106Ω

Vasquez · Accepted Answer

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)(2.5×10−6F)=150Hz

(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 60

Answered question

Answer & Explanation

New Questions in Other