Question

In the circuit diagram shown $X_C=100\Omega ,X_L=200\Omega$ and $R=100\Omega .$ The effective through the source is:

• A. $2A$
• B. $\sqrt{2}A$
• C. $4A$
• D. $2\sqrt{2}A$

Answer 1

The correct option is D $2\sqrt{2}A$

$\begin{array}{c}TheeffectiveinpedanceofseriesLCcircuit\\ X=\sqrt{{\left(Xl-X_c\right)}^2}=\sqrt{{\left(200-100\right)}^2}=100\Omega \\ Thisisparallelwithresistor\\ Sonetreac\tan e\\ \frac{1}{Z^{\prime }}=\sqrt{{\left(\frac{1}{100}\right)}^2+{\left(\frac{1}{100}\right)}^2}\\ Z^{\prime }=\sqrt{5000}=10\sqrt{20}\Omega \\ V=IR\\ I=\frac{200}{10\sqrt{50}}=2\sqrt{2}\end{array}$

Option $D$ is correct .