# 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

$\overline{)\begin{array}{rcl}{\mathbf{X}}_{\mathbf{C}}& {\mathbf{=}}& {\mathbf{X}}_{\mathbf{L}}\\ \frac{\mathbf{1}}{{\mathbf{\omega }}_{\mathbf{1}}\mathbf{C}}& {\mathbf{=}}& {\mathbf{\omega }}_{\mathbf{1}}\mathbf{L}\\ {{\mathbf{\omega }}_{\mathbf{1}}}^{\mathbf{2}}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{L}\mathbf{C}}\end{array}}$

a.

At frequency, ω2,

XL = ω2L = 2ω1L

###### 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?