Question

23) Given a filtering circuit, you are asked to connect the following components in series. A 4mH inductor, 6 microfarad capacitor, and a 200 S2. They car connected with a 30 V voltage source that has angular frequency of 250 rad/s. i) What is the impedance of the entire circuit? j) What are the voltages across the resistor and inductor? k) Calculate the phase angle

Answer 1

Part 1

Net impedance of the circuit is

$Z= \sqrt{R^2 + \left ( \omega L-\frac{1}{\omega C} \right )^2}$

w = 250rad/S

C 6μF

$R =200 \Omega$

So,

$Z= \sqrt{200^2 + \left ( (250) (4\times 10^{-3})-\frac{1}{(250)(6\times 10^{-6})} \right )^2}$

$Z = 695.063 \Omega$

Net current is

$I = \frac{V}{Z}$

$I = \frac{30}{695.063}$

Now voltages

$V_C =I \omega L$

$V_C =(0.043)(250) (4 \times 10^{-3})$

Part 3

phase angle

$cos(\phi) = \frac{R}{Z}$

$cos(\phi) = \frac{200}{695.063}$

$\phi = 73.27$