Answer :
The frequency of the resulting oscillation is approximately 25.8 Hz.
An LC circuit consists of an inductor (L) and a capacitor (C) connected in series. When the switch in the circuit is closed, the initial energy stored in the charged capacitor starts transferring to the inductor. This transfer creates an oscillation in the circuit, with the energy shifting back and forth between the inductor and the capacitor.
To find the angular frequency (ω) of the resulting oscillation, we can use the formula:
ω = 1 / √(LC)
where L is the inductance and C is the capacitance. Given that the inductance is 105mH (105 x 10^-3 H) and the capacitance is 55μF (55 x 10^-6 F), we can substitute these values into the formula:
ω = 1 / √((105 x 10^-3) x (55 x 10^-6))
Simplifying the calculation:
ω = 1 / √(5.775 x 10^-6)
ω ≈ 162 rad/s
Therefore, the angular frequency of the resulting oscillation is approximately 162 rad/s.
To find the frequency (f) of the resulting oscillation in Hertz, we can use the formula:
f = ω / (2π)
Substituting the value of ω we calculated earlier:
f = 162 / (2π)
Using an appropriate calculator, we can find that:
f ≈ 25.8 Hz
Therefore, the frequency of the resulting oscillation is approximately 25.8 Hz.
Please note that this is just one example of solving this problem. Depending on the specific values given in the problem, the calculations may vary. It is important to carefully read and understand the given information in order to solve the problem accurately.
Learn more about angular frequency (ω)
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