Answer:
Impedance = 8,274.02Ω
Phase angle = 170.48°
rms current = 0.0978A
Explanation:
The impedance of the LRC circuit is expressed as;
[tex]Z = \sqrt{R^2+(X_L-X_C)^2} \\[/tex]
R is the resistance
XL is the inductive reactance = 2πfL
XC is the capacitive reactance = 1/2πfC
f is the frequency
L is the inductance
C is the capacitance
Given
L = 22.3 mH = 0.0223H
R = 8.16 kΩ = 8160Ω
C = 5750 pF = 5750 * 10^-12
Get XL;
XL = 2πfL
XL= 2π(10*10^3)(0.0223)
XL = 2(3.14)(223)
XL = 1400.44Ω
Get XC;
XC = 1/2πfC
XC = 1/2(3.14)(10,000)(5750 * 10^-12)
XC = 1/0.0003611
XC = 2,769.32Ω
Get the impedance;
[tex]Z = \sqrt{R^2+(X_L-X_C)^2} \\Z = \sqrt{(8160)^2+(1400.44-2769.32)^2} \\Z = \sqrt{(8160)^2+(-1,368.87)^2} \\Z = \sqrt{66,585,600+1,873,821.44} \\Z = \sqrt{68,459,421.44} \\Z = 8,274.02 ohms\\[/tex]
Get the phase angle;
[tex]\theta = tan^{-1}\frac{XL-XC}{R}\\\theta = tan^{-1}\frac{-1368.87}{8160}\\\theta = tan^{-1}(-0.1677)\\\theta = -9.52^0\\\theta = 180-9.52\\\theta = 170.48^0[/tex]
Get the rms current
I = V/Z
I = 809/8274.02
I = 0.0978A
