[tex]f_{0}=159.2KHz[/tex]
In order to solve this problem we have to use the resonance frecuency equation [tex]f_{0}=\frac{1}{2\pi \sqrt{LC}}[/tex], at this frecuency in a LC circuit the capacitor and the inductor have the same reactance. So:
With C = 1.0μF and L = 1.0μH
[tex]f_{0}=\frac{1}{2\pi \sqrt{(1.0x10^{-6}F)(1.0x10^{-6}H)}}\\f_{0}=159155Hz\\f_{0}=159.2KHz[/tex]
The 1.0 μf capacitor and a 1.0 μh inductor have the same reactance at [tex]f_{0}[/tex] = 159.15 KHz.
A capacitor is a device that stores electrical energy.
An inductor is a device that stores electrical energy in the form of magnetic field.
Now, putting value of capacitor C and inductor L in above equation we get,
[tex]f_{0}[/tex] = [tex]\frac{1}{2\pi \sqrt{LC} }[/tex]
[tex]f_{0}[/tex] = [tex]\frac{1}{2\pi \sqrt{(1.0x10^{-6})(1.0x10^{-6}) } }[/tex]
[tex]f_{0}[/tex] = 159155 Hz.
Thus, for same reactance the frequency will be 159.2 KHz.
Learn more about resonance frequency here -
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