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An inductor is a passive two-terminal device that stores energy in a magnetic field when current passes through it. When an inductor is attached to an AC supply, the resistance produced by it is called inductive reactance (X_L).

A capacitor is a device consisting of two conductors in close proximity that are used to store electrical energy. These conductors are insulated from each other. When a capacitor is attached to an AC supply, the resistance produced by it is called capacitive reactance (X_C).

Frequency of source, f₁ = 60 Hz, and f₂ = 600 Hz

The inductance of the coil, L = 0.45 H

Capacitance of capacitor, C = 2.50 µF

Inductive reactance is given by,$X_L=2\mathrm{Ï€}fL$

For f₁ = 60 Hz,

$X_L=2\mathrm{Ï€}fL=2\mathrm{Ï€}\left(60Hz\right)(0.45H)=170\mathrm{Î\copyright }$

For f₂ = 600 Hz,

$X_L=2\mathrm{Ï€}fL=2\mathrm{Ï€}\left(600Hz\right)(0.45H)=1700\mathrm{Î\copyright }$

Therefore, the Inductive reactance is 170 Ω when frequency of the source is 60 Hertz and 1700 Ω when the frequency of the source is 600 Hertz.

Capacitive reactance is given by,$X_C=\frac{1}{2\mathrm{Ï€´Ú°ä}}$

For f₁ = 60 Hz,

$X_C=\frac{1}{2\mathrm{Ï€´Ú°ä}}=\frac{1}{2\mathrm{Ï€}\left(60\mathrm{Hz}\right)\left(2.5*{10}^{-6}\mathrm{F}\right)}=1060\mathrm{Î\copyright }$

For f₂ = 600 Hz,

$X_C=\frac{1}{2\mathrm{Ï€´Ú°ä}}=\frac{1}{2\mathrm{Ï€}\left(600\mathrm{Hz}\right)\left(2.5*{10}^{-6}\mathrm{F}\right)}=106\mathrm{Î\copyright }$

Therefore, the Capacitive reactance is 1060 Ω when frequency of the source is 60 Hertz and 160 Ω when the frequency of the source is 600 Hertz.

It is given that Inductive resistance is equal to Capacitive resistance, which means,

$$\begin{gathered} X_L=X_C \\ 2\mathrm{Ï€´Ú³¢}=\frac{1}{2\mathrm{Ï€´Ú°ä}} \\ \mathrm{f}=\frac{1}{2\mathrm{Ï€}\sqrt{\mathrm{LC}}} \\ \mathrm{f}=\frac{1}{2\mathrm{Ï€}\sqrt{\left(0.45\mathrm{H}\right)\left(2.5*{10}^{-6}\mathrm{F}\right)}}=150\mathrm{Hz} \end{gathered}$$

Therefore, the frequency at which Inductive resistance gets equal to Capacitive resistance is 150 Hertz.