Answer:
(a) 4.04 ohm
(b) 6.93 A
(c) 8.53°
Explanation:
f = 12 kHz = 12000 Hz
Vo = 28 V
R = 4 ohm
L = 30 micro Henry = 30 x 10^-6 H
C = 8 micro Farad = 8 x 10^-6 F
(a) Let Z be the impedance
[tex]X_{L} = 2\pi fL=2\times3.14\times12000\times30\times10^{-6}= 2.26 ohm[/tex]
[tex]X_{c} = \frac{1}{2\pi fC}=\frac{1}{2\times3.14\times12000\times8\times10^{-6}}= 1.66 ohm[/tex]
[tex]Z = \sqrt{R^{2}+(X_{L}-X_{C})^{2}}=\sqrt{4^{2}+\left ( 2.26-1.66 \right )^{2}}[/tex]
Z = 4.04 Ohm
(b) Let Io be the amplitude of current
[tex]I_{o}=\frac{V_{o}}{Z}[/tex]
[tex]I_{o}=\frac{28}{4.04}[/tex]
Io = 6.93 A
(c) Let the phase difference is Ф
[tex]tan\phi = \frac{X_{L}-X_{C}}{R}[/tex]
[tex]tan\phi = \frac{2.26-1.66}{4}[/tex]
tan Ф =0.15
Ф = 8.53°
