Problem: At a frequency ω 1 the resistance of a certain capacitor equals that of a certain inductor.a. If the frequency is changed to ω 2=2ω 1, what is the ratio of the reactance of the inductor to that of the capacitor? What reactance is larger?b. If the frequency is changed to ω 3=ω 1/3, what is the ratio of the reactance of the inductor to that of the capacitor? Which reactance is larger?c. If the capacitor and inductor are placed in series with a resistor of resistance R to form a series L-R-C circuit, what will be the resonance angular frequency of the circuit?

FREE Expert Solution

At the given frequency, ω1

XC=XL1ω1C=ω1Lω12=1LC

a.

At frequency, ω2,

 XL = ω2L = 2ω1L

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Problem Details

At a frequency ω 1 the resistance of a certain capacitor equals that of a certain inductor.

a. If the frequency is changed to ω 2=2ω 1, what is the ratio of the reactance of the inductor to that of the capacitor? What reactance is larger?

b. If the frequency is changed to ω 3=ω 1/3, what is the ratio of the reactance of the inductor to that of the capacitor? Which reactance is larger?

c. If the capacitor and inductor are placed in series with a resistor of resistance R to form a series L-R-C circuit, what will be the resonance angular frequency of the circuit?