91Ó°ÊÓ

Inductor is $L=45\mathrm{mH}$.

Reactance is$R=1.30\text{°ìΩ}$ .

Reactance withstands currents without loss of power, unlike resistors. Inductive reactance increases with frequency and inductance. Capacitive reactance decreases with frequency and capacitance. Impedance represents the total opposition provided by reactance and resistance.

Formula:

The inductive reactance is,

$X_L=2\mathrm{Ï€}fL$

The capacitive reactance is,

$X_c=\frac{1}{2\mathrm{Ï€}fC}$

Write inductive capacitance as

$\begin{array}{rcl}{X}_L& =& 2\mathrm{π}fL\\ 1300& =& 2×3.14×f×45×{10}^{-3}\\ f& =& 4.6\mathrm{kHz}\end{array}$

Hence, the operating frequency is$4.6\mathrm{kHz}$ .

As given that $X_L=X_c$

Therefore,

$\begin{array}{rcl}2\mathrm{Ï€}fL& =& \frac{1}{2\mathrm{Ï€}fC}\\ f^2& =& \frac{1}{4{\mathrm{Ï€}}^{2}LC}\end{array}$

$\begin{array}{rcl}C& =& \frac{L}{\frac{1}{4{\mathrm{Ï€}}^2{L}^2{f}^2}}\\ & =& \frac{L}{X_l^2}\end{array}$

$\begin{array}{rcl}C& =& \frac{45×{10}^{-3}}{{\left(1300\right)}^2}\\ & =& 26.62×{10}^{-9}\mathrm{F}\\ & =& 26.62\mathrm{nF}\end{array}$

Hence, the capacitance is$26.62\mathrm{nF}$.

When frequency is double

The inductive capacitance is,

$\begin{array}{rcl}{X}_L& =& 2×3.14×9×{10}^3×45×{10}^{-3}\\ & =& 2.6\mathrm{°ìÎ\copyright }\end{array}$

If frequency is doubled, then reactance of inductor is $2.6\mathrm{°ìÎ\copyright }$.

If frequency is doubled,the reactance of capacitor:

$\begin{array}{rcl}{X}_c& =& \frac{1}{2\mathrm{Ï€}fC}\\ & =& \frac{1}{2×3.14×9×{10}^3×26.62×{10}^{-9}}\\ & =& 0.65\mathrm{°ìÎ\copyright }\end{array}$

Hence, if frequency is doubled, then reactance of capacitor is $0.65\mathrm{°ìÎ\copyright }$.