An LC circuits if formed by an inductor and a capacitor. The charge on the capacitor and the current through the inductor both vary sinusoidally with time. Also, energy is transferred between magnetic energy in the inductor and electrical energy in the capacitor. But what happens with the frequency if the inductance is quadrupled? that is, if initially the inductance is [tex]L[/tex] and the frecuency [tex]f=2000Hz[/tex] if now [tex]L_{New}=4L[/tex] What will the frequency be? Well, we know that the frequency, inductance and capacitance are related as:
[tex]f=\frac{1}{2\pi}\sqrt{\frac{1}{LC}}[/tex]
and this equals 2000Hz. If now L is quadrupled:
[tex]f_{1}=\frac{1}{2\pi}\sqrt{\frac{1}{4LC}}=\frac{1}{2\pi}\sqrt{\frac{1}{4}}\sqrt{\frac{1}{LC}} \\ \\ \therefore f_{1}=(\frac{1}{2})\frac{1}{2\pi}\sqrt{\frac{1}{LC}} \\ \\ \\ Since \ f=\frac{1}{2\pi}\sqrt{\frac{1}{LC}} \ then: \\ \\ f_{1}=\frac{1}{2}f \therefore f_{1}=\frac{2000}{2} \\ \\ \therefore \boxed{f_{1}=1000Hz}[/tex]
Finally, if L is quadrupled the frequency is half the original frequency and equals 1000Hz
The frequency be if the inductance is quadrupled is mathematically given as
f1=1000Hz
Question Parameter(s):
An lc circuit oscillates at a frequency of 2000 Hz.
Generally, the equation for the Freqency is mathematically given as
[tex]f=\frac{1}{2\pi}\sqrt{\frac{1}{LC}}[/tex]
Therefore
[tex]f_{1}=\frac{1}{2\pi}\sqrt{\frac{1}{4LC}}=\frac{1}{2\pi}\sqrt{\frac{1}{4}}\sqrt{\frac{1}{LC}} \\\\ f_{1}=(\frac{1}{2})\frac{1}{2\pi}\sqrt{\frac{1}{LC}} \\ \\ f_{1}=\frac{2000}{2} \\[/tex]
f1=1000Hz
In conclusion
f1=1000Hz
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