Question

In a medium ware broadcast radio can be tuned in frequency range $300kHz$ to $1200kHz$ in circuit of this radio effective inductance is $300cH$, what range of variable capacitor?

Answer 1

Given, ${\alpha }_1=300\times {10}^{3}Hz$

${\alpha }_2=1200\times {10}^{3}Hz$

$L=300\mu H=300\times {10}^{-6}H$

${\alpha }_1=\frac{1}{2\pi \sqrt{L{C}_1}}$

$C_1=\frac{1}{4\pi L{\alpha }_1^2}$

or, $C_1=\frac{1}{4{\pi }^2\times L\times {(360\times {10}^3)}^2}$

$=\frac{1}{4{\left(3.14\right)}^2\times 3.06\times {10}^{-6}{(300\times {10}^3)}^2}$

$=9.39\times {10}^{-8}$

$=93pF$

In the same way,

$C_2=\frac{1}{{4\pi }^{2}L{\alpha }_2^2}$

$=\frac{1}{{4\pi }^2\times 300\times {10}^{-6}\times {(1200\times {10}^{+3})}^2}$

$=\frac{1}{{4\pi }^2(300\times {10}^{-6}){(1200\times {10}^{+3})}^2}$

$=\frac{1}{4{\left(3.14\right)}^2\times (300\times {10}^{-6})\times {(1200\times {10}^3)}^2}$

$=58pF$.