Question

What inductance must be connected to a $ 17 \,pF $ capacitor in an oscillator capable of generating $ 550 \,nm $ electromagnetic waves?

• A. $ 2.3 \times 10^{-25} \, H $
• B. $ 4.2 \times 10^{-23} \, H $
• C. $ 2.6 \times 10^{-22} \, H $
• D. $ 5.0 \times 10^{-21} \, H $

Answer 1

Answer: (D)

Given, $C = 17 \,pF$
Wavelength of $EM$ wave $\lambda=550\,nm$
$=550\times 10^{-9}\,m$
For $EM$ wave $v = c =3 \times 10^{8} m/s$
$f=\frac{v}{\lambda}=\frac{c}{\lambda}=\frac{3\times10^{8}}{550\times10^{-9}}=5.4\times10^{14}Hz$
Now, frequency of oscillation $f =\frac{1}{2\pi \sqrt{LC}}$
$5.4\times10^{14}=\frac{1}{2\times3.14\sqrt{L\times17\times10^{-12}}}$
$L=\frac{1 }{ 2\times3.14\times5.4\times10^{14})^{2}\times17\times10^{-12}}$
$=5\times 10^{-2}\,H$