Physics - EMI/AC Question with Solution | TestHub

$\omega =100$ rad/sec

phase difference between $e$ and $i$ is given by

$\tan \theta =\frac{X}{R}\therefore \theta =\frac{\pi }{4}$

so $\tan \theta =\tan \frac{\pi }{4}=1$

in case of $RL$ circuit $X=X_L=\omega L$

And in case of $R\mathrm{C}$ circuit $X=X_c=\frac{1}{\omega c}$

For option $\left(A\right):$ $R=1000\Omega$ and

$X_C=\frac{1}{\omega \mathrm{C}}=\frac{1}{\left(100\right)\left(1\times 10^{-6}\right)}=10000\Omega$
$\tan \theta =\frac{X_C}{R}\ne 1$
For option $\left(B\right):$ $R=10^3\Omega$ and

$X_L=L\omega =\left(10^{-3}\right)\left(100\right)=0.1\Omega$

$\tan \theta =\frac{X_L}{R}\ne 1$
For option $\left(C\right):R=1000\Omega$ and

$X_L=\omega L=\left(100\right)\left(10\right)=1000\Omega$
$\tan \theta =\frac{X_L}{R}\ne 1$
For option$\left(D\right):R=1k\Omega =1000\Omega$ and

$X_C=\frac{1}{\omega \mathrm{C}}=\frac{1}{\left(100\right)\left(10\times 10^{-6}\right)}=1000\Omega$
$\tan \theta =\frac{X_C}{R}=1;\theta =45^o$