Answer:
(a) 14.88 ohm
(b) 1.88 A
(c) -74.4°
Explanation:
Vo = 28 V
f = 12 kHz = 12000 Hz
R = 4 ohm
L = 30 micro henry = 30 x 10^-6 H
C = 800 nF = 800 x 10^-9 F
(a)
The inductive reactance,
XL = 2 π f L = 2 x 3.14 x 12000 x 30 x 10^-6 = 2.26 ohm
The capacitive reactance
[tex]X_{c}=\frac{1}{2\pi fC}=\frac{1}{2 \times 3.14 \times 12000 \times 800 \times 10^{-9}}[/tex]
Xc = 16.59 ohm
Let the impedance is Z.
[tex]Z=\sqrt{4^{2}+\left ( 2.26-16.59 \right )^{2}}[/tex]
Z = 14.88 ohm
(b)
The formula for the amplitude of current
[tex]I_{o}=\frac{V_{o}}{Z}=\frac{28}{14.88}[/tex]
Io = 1.88 A
(c)
Let the phase difference is Ф
[tex]tan\phi =\frac{X_{L}-X_{C}}{R}=\frac{2.26-16.59}{4}=-3.5825[/tex]
Ф = -74.4°
