It is desired to make the net impedance of the parallel comb

It is desired to make the net impedance of the parallel combination of an inductance and a resistance completely resistive at 1 MHz by adding a capacitor in series with it, as shown in the figure below. What is the required value of C to achieve this?

Solution

f=1*10^6 HZ

XL=jwL=j2*3.14*1*10^6*300*10^-6=j1884.95 ohms

Zeq=-jXc+[(500*j1884.95)/(500+j1884.95)]

467.13+j123.9-jXc=467.13

Xc=123.9

1/(wC)=123.9

1/(2*3.14*1*10^6*C)=123.9

C=1.2845*10^-9 FARADS.