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Answer :
Resonant frequency refers to the natural frequency at which an object or system vibrates or oscillates with the maximum amplitude. It is the frequency at which the object or system resonates or responds most strongly to an external force or stimulus.
The frequency of oscillation for the LC circuit is given as 38.8 GHz and the capacitance is given as 1.20 pF. To find the required inductance for the circuit to resonate at this frequency, we can use the formula for the resonant frequency of an LC circuit:
f = 1 / (2π√(LC))
Where f is the frequency, L is the inductance, and C is the capacitance.
In this case, we are given f = 38.8 GHz and C = 1.20 pF. We can rearrange the formula to solve for L:
L = (1 / (4π²f²C))
Substituting the given values into the formula, we get:
L = (1 / (4π²(38.8 GHz)²(1.20 pF)))
Now we need to convert the frequency from GHz to Hz and the capacitance from pF to F, as the formula requires SI units.
1 GHz = 10^9 Hz
1 pF = 10^-12 F
Converting the values, we have:
L = (1 / (4π²(38.8 × 10^9 Hz)²(1.20 × 10^-12 F)))
Simplifying the equation and calculating the value, we find:
L ≈ 1.146 nH
Therefore, the required inductance for the LC circuit to resonate at a frequency of 38.8 GHz with a capacitance of 1.20 pF is approximately 1.146 nH.
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