Question

7) Given a timing circuit, you are asked to connect the following components in series. A 6-microfarad capacitor, and a 200 12. They car connected with a 30 V voltage source that has angular frequency of 250 rad/s. a) What is the impedance of the entire circuit? b) What is voltage across both the resistor and capacitor? c) Calculate the phase angle d) What quadrant would you find this angle?

Answer Questions A, B, C and D.

Answer 1

I 카 R

Given,

Resistance is

Ꭱ = 200 Ꮂ

Capacitance is

C = 6 F = 6 * 10-6 F

Voltage source is

Angular frequency of source is

w = 250 rad/ os

a)

Capacitive reactance is

$X_C = \frac{1}{C\omega} = \frac{1}{6 * 10^{-6} * 250} = 666.67 \ \Omega$

Impedance of the entire circuit is

$\\Z = \sqrt{R^2 + X_C^2} \\\\Z = \sqrt{200^2 + 666.67^2} \\\\Z = \sqrt{484448.89} \\\\Z = 696.02 \ \Omega$

b)

Current in the circuit is $I = \frac{V}{Z} = \frac{30}{696.02} = 0.0431 \ A$

Voltage across the resistor is

Voltage across the capacitor is

c)

Phase angle is

$\theta = \tan^{-1}(\frac{X_C}{R}) = \tan^{-1}(\frac{666.67}{200}) = 73.3\degree$

d) As it is a purely RC circuit, the phase angle will be in the Fourth Quadrant