23 June, 23:29

# Use phasor techniques to determine the impedance seen by the source given that R = 4 Ω, C = 12 μF, L = 6 mH and ω = 2000 rad/sec. Then determine the current supplied by the source given that V = 12 <0o v. The equivalent impedance seen by the source is Z = ∠ o Ω. (Round the magnitude to three decimal places and the angle to two decimal places.) The current supplied by the source is I = ∠ o A. (Round the magnitude to three decimal places and the angle to two decimal places.)

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1. 23 June, 23:45
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Z = 29.938Ω ∠22.04°

I = 2.494A

Explanation:

Impedance Z is defined as the total opposition to the flow of current in an AC circuit. In an R-L-C AC circuit, Impedance is expressed as shown:

Z² = R² + (Xl-Xc) ²

Z = √R² + (Xl-Xc) ²

R is the resistance = 4Ω

Xl is the inductive reactance = ωL

Xc is the capacitive reactance =

1/ωc

Given C = 12 μF, L = 6 mH and ω = 2000 rad/sec

Xl = 2000*6*10^-3

Xl = 12Ω

Xc = 1/2000*12*10^-6

Xc = 1/24000*10^-6

Xc = 1/0.024

Xc = 41.67Ω

Z = √4² + (12-41.67) ²

Z = √16+880.31

Z = √896.31

Z = 29.938Ω (to 3dp)

θ = tan^-1 (Xl-Xc) / R

θ = tan^-1 (12-41.67) / 12

θ = tan^-1 (-29.67) / 12

θ = tan^-1 - 2.47

θ = - 67.96°

θ = 90-67.96

θ = 22.04° (to 2dp)

To determine the current, we will use the relationship

V = IZ

I = V/Z

Given V = 12V

I = 29.93/12

I = 2.494A (3dp)