Question

For the circuit shown in the figure, the time constant RC = 1 ms. The input voltage is $v_i\left(t\right)=\sqrt{20}\sin {10}^{3}t.$ The output voltage $v_0\left(t\right)$ is equal to

• A. $sin({10}^{3}t-45°)$
• B. $sin({10}^{3}t+45°)$
• C. $sin({10}^{3}t-53°)$
• D. $sin({10}^{3}t+53°)$

Answer 1

The correct option is A $sin({10}^{3}t-45°)$

$v_0\left(t\right)=\frac{\frac{1}{j\omega C}}{R+\frac{1}{j\omega C}}{v}_i\left(t\right)=\frac{1}{1+j\omega CR}$ $\sqrt{2}\sin {10}^{3}t$

$=\frac{1}{1+j\times {10}^3\times {10}^{-3}}\sqrt{2}\sin {10}^{3}t$

$v_0\left(t\right)=\sin ({10}^{3}t-45{}^{\circ })$