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enter image description hereI am working on the question in the image attached, and I am having trouble with part b)

I found part a by using the formula of resonant frequency for a first order LC filter: w=1/sqrt(LC), and by rearranging for L, and plugging in w=108 x 10^6 x 2pi, and C=25 x 10^-12.

For part b, I have rearrange the same equation for C, and have used the inductance found in a), and plugged in w=88 x 10^6 x 2pi, however this is wrong.

Any ideas is greatly appreciated. Thank you very much.

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  • \$\begingroup\$ Think about the capacitor in parallel.. Now you have to consider two caps. Not just one.. Sum of two capacitances will contribute for 88 MHz.. Do not ignore C already present with value of 25 pF \$\endgroup\$ – Umar Jun 11 '18 at 3:09
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I solved the first equation and came up with 86.866 nH @ 25 pF for L.

For the second equation I used; $$C = \frac{1}{L\cdot(F^2)\cdot(pi^2)\cdot 4}$$ = 37.649 pF.

The final answer is 12.------. Sorry, but you need to solve the last digits yourself so you understand the math. If you plan this as a career, it pays to build up a library or cheat-sheet of these resonance equations. There are a lot of them.

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You have solved for C, which is the capacitance you used with the inductance to get to 88 MHz. In your circuit, you have C (which you solved for initially), plus an added capacitance Cv. So Cv is the capacitance you add to the original C (from step A) to get the total C you got in step B.

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