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

Question

What inductance must be connected to a 17 pF capacitor in an oscillator capable of generating 550 nm electromagnetic waves? (A)  2.3 × 10-25 H  (B)  4.2 × 10-23 H  (C)  2.6 × 10-22 H  (D)  5.0 × 10-21 H

Tardigrade Admin · Accepted Answer

Given, C = 17 pF Wavelength of EM wave λ=550 nm =550× 10-9 m For EM wave v = c =3 × 108 m/s f=(v/λ)=(c/λ)=(3×108/550×10-9)=5.4×1014Hz Now, frequency of oscillation f =(1/2π √LC) 5.4×1014=(1/2×3.14√L×17×10-12) L=(1 / 2×3.14×5.4×1014)2×17×10-12) =5× 10-2 H

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

$2.3 \times 1 0^{- 25} H$

$4.2 \times 1 0^{- 23} H$

$2.6 \times 1 0^{- 22} H$

$5.0 \times 1 0^{- 21} H$

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

2.3×10−25H

4.2×10−23H

2.6×10−22H

5.0×10−21H

Given, C=17pF Wavelength of EM wave λ=550nm =550×10−9m For EM wave v=c=3×108m/s f=λv​=λc​=550×10−93×108​=5.4×1014Hz Now, frequency of oscillation f=2πLC​1​ 5.4×1014=2×3.14L×17×10−12​1​ L=2×3.14×5.4×1014)2×17×10−121​ =5×10−2H

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

$2.3 \times 1 0^{- 25} H$

$4.2 \times 1 0^{- 23} H$

$2.6 \times 1 0^{- 22} H$

$5.0 \times 1 0^{- 21} H$