Respuesta :
Answer:
[tex]C_2=\frac{C_1}{4}[/tex]
Explanation:
Given:
Initial capacitance, C = C₁
Initial Frequency, F₁ = 600kHz
Final Frequency, F₂ = 1200kHz
let the adjusted capacitance be, C₂
Now
the frequency (f) is given as:
[tex]f={\frac{1}{2\pi \sqrt{LC}}}[/tex]
where, L = inductance (same for the same material)
thus substituting the values we have
[tex]600={\frac{1}{2\pi \sqrt{LC_1}}}[/tex] ...............(1)
and
[tex]1200={\frac{1}{2\pi \sqrt{LC_2}}}[/tex] ..............(2)
dividing the equation 1 with 2, we get
[tex]\frac{600}{1200}=\frac{{\frac{1}{2\pi \sqrt{LC_1}}}}{{\frac{1}{2\pi \sqrt{LC_2}}}}[/tex]
or
[tex]\frac{1}{2}=\sqrt{\frac{C_2}{C_1}}[/tex]
or
[tex]\frac{C_2}{C_1}=\frac{1}{4}[/tex]
or
[tex]C_2=\frac{C_1}{4}[/tex]
hence, the new capacitance C, must be one-fourth times the initial capacitance
The capacitance for the frequency of 1200 kHz must be one-fourth times the capacitance for the frequency of 800 kHz.
What is capacitance?
Capacitance is the ability of a circuit to store energy in the form of an electrical charge.it is an energy-storing device. generally, it is defined by the ratio of electric charge stored to the potential difference.
Given:
Initial capacitance is C
Capacitance for the frequency of 1200 kHz is [tex]\rm{C=C_1}[/tex]
The capacitance for the frequency of 800 kHz is [tex]\rm{C=C_2}[/tex]
The frequency (f) is given by
[tex]f=\frac{1}{2\pi \sqrt{LC} }[/tex]
The capacitance for the frequency of 1200 kHz finds by
[tex]f_1=\frac{1}{2\pi \sqrt{LC_1} }[/tex]
[tex]1200=\frac{1}{2\pi \sqrt{LC_1} }[/tex] ------------------1
The capacitance for the frequency of 800 kHz
[tex]f_2=\frac{1}{2\pi \sqrt{LC_2} }[/tex]
[tex]600=\frac{1}{2\pi \sqrt{LC_2} }[/tex] ------------------2
On dividing the equation 2 by 1
[tex]\frac{1}{2} =\sqrt{\frac{C_2}{C_1} }[/tex]
[tex]{\frac{C_2}{C_1} }=\frac{1}{4}[/tex]
[tex]C_2=\frac{C_1}{4}[/tex]
Hence the capacitance for the frequency of 1200 kHz must be one-fourth times the capacitance for the frequency of 800 kHz.
Learn more about the capacitance refer to the link
https://brainly.com/question/12356566
