Question

In the given circuit, the AC source has $\omega=100\, rad / s$. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

• A. The current through the circuit, $I$ is $0.3\, A$.
• B. The current through the circuit, $I$ is $0.3 \sqrt{2} A$.
• C. The voltage across $100\, \Omega$ resistor $=10 \sqrt{2} V$.
• D. The voltage across $50 \,\Omega$ resistor $=10\, V$.

Answer 1

Answer: (A), (C)

From the given circuit, we have
$I_{\text {capacitance }}=\frac{20}{100 \sqrt{2}}$ (progress ahead of the voltage by $+\pi / 4$ )
$I_{\text {inductive }}=\frac{20}{50 \sqrt{2}}$ (lagging behind the voltage by $-\pi / 4$ )
Therefore,
$I=\sqrt{I_{1}{ }^{2}+I_{2}{ }^{2}}=\sqrt{\frac{1}{10}} \sim 0.3$
$V_{100 \,\Omega}=\frac{20}{100 \sqrt{2}} \times 100=10 \sqrt{2} V .$