Max and min frequencies of a capacitor

[laminatedevildoll]

A variable capacitor with a range from 10 to 365 p is used with a coil to form a variable frequency LC circuit t0 tune the input to a radio.

a. What ratio of max and min frequencies may be obtained with such capcitor.

I used that $$\omega=\frac 1{\sqrt(LC)}$$ to get the ratio of max to min frequencies.

b. If this circuit is to obtain frequencies from 0.54 MHz to 1.60 mHz, the rato computed is too large. By adding a capacitor in parallel, this range may be adjused. What should the capacitance of this added be?

I said that $$C_{eq} = C_{old}+C_{new}$$

I have to compute what $$C_{new}$$. From part 1, I know my $$C_{old}$$. But, how do I find $$C_{eq}$$ first? I am thinking that I have to compute that using the frequencies, but how do I get L?

 

[inha]

You're not doing anything to the coil, are you? Why would L change from what it was before adding the second capacitor?

 

[laminatedevildoll]

I thought that the L canceled out when I was doing the ratio before. So, would I use L from part A? Do I solve for L?

 

[inha]

Use the earlier inductance and the frequencies the circuit is supposed to be able to deal with. Solve for C_eq and solve for C_new.

 

[Gokul43201]

You are given $\omega_1, ~\omega _2$. You know $C_{old}$. The unknowns are $L,~C_{eq},~C_{new}$.

You have three equations in 3 unknowns...