Question

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

• A. The current through the circuit, $I$ is $0.3A$.
• 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 $=10V$.

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,
$I=\sqrt{I_1{}^2+I_2{}^2}=\sqrt{\frac{1}{10}}\sim 0.3$
$V_{100\Omega }=\frac{20}{100\sqrt{2}}\times 100=10\sqrt{2}V.$