Question 487: AC fundamentals

Question

Which of the following statement is correct regarding the AC circuit shown in the adjacent figure?

Accepted Answer

In the given AC circuit, the reactance of the capacitor and the inductor are equal, which means:
$$ X_C = X_L $$
Since their effects cancel each other, the total impedance of the circuit becomes equal to the resistance $ R $:
$$ Z = R = 2 \, \Omega $$
Now, using OhmÃ¢ÂÂs law for AC circuits, the root-mean-square (rms) current can be calculated as:
$$ i_{	ext{rms}} = \frac{V_{	ext{rms}}}{Z} $$
Substitute the given values:
$$ i_{	ext{rms}} = \frac{100 / \sqrt{2}}{2} = 25 \sqrt{2} \, 	ext{A} $$
Because $ X_C = X_L $, the current and voltage are in phase. Hence, the phase difference is:
Zero degrees $(0^\circ)$.
Now, the average power consumed in an AC circuit is given by:
$$ P = V_{	ext{rms}} \, i_{	ext{rms}} \, \cos \phi $$
Substituting the values:
$$ P = \frac{100}{\sqrt{2}} 	imes 25 \sqrt{2} 	imes \cos 0^\circ = 2500 \, 	ext{W} $$
Therefore, the average power consumed by the circuit is
2500 W
.

Answer

The rms value of current through the circuit is $i_{	ext {rms }}=5 \sqrt{2} \mathrm{~A}$

Answer

The phase difference between source emf and current is $\phi=\cos ^{-1}\left(\frac{1}{3}\right)$

Answer

Average power dissipated in the circuit is 500 W

Answer

None of the above

AC fundamentals

Which of the following statement is correct regarding the AC circuit shown in the adjacent figure?

Choose the correct answer: