Physics - EMI/AC Question with Solution | TestHub

The formula to calculate the inductive impedance of the circuit is given by

$X_L=\omega L ...\left(1\right)$

The formula to calculate the capacitive impedance of the circuit is given by

$X_C=\frac{1}{\omega C} ...\left(2\right)$

The formula to calculate the total impedance of the circuit can be written as

$\begin{array}{rcl}Z& =& \sqrt{R^2+{\left(X_c-X_L\right)}^2}\\ & =& \sqrt{R^2+{\left(\frac{1}{\omega C}-\omega L\right)}^2} ...\left(3\right)\end{array}$

Substitute the values of the given parameters into equation (3) to calculate the required net impedance of the circuit.

$\begin{array}{rcl}Z& =& \sqrt{{\left(10 \mathrm{\Omega }\right)}^2+{\left(\frac{1}{2\pi \times 50 \mathrm{Hz}\times {\displaystyle \frac{{10}^3}{\pi }}\times {10}^{-6} \mathrm{F}}-2\pi \times 50 \mathrm{Hz}\times \frac{50}{\pi }\times {10}^{-3} \mathrm{H}\right)}^2}\\ & =& \sqrt{100+25} \mathrm{\Omega }\\ & =& \sqrt{125} \mathrm{\Omega }\\ & =& 5\sqrt{5} \mathrm{\Omega }\end{array}$