Question
Download Solution PDFThe following is an RL filter circuit with the inductance L = 400 mH and the input voltage Vin = (20.0 V) sin ω, where ω = 200 rad/s. For what value of R will the output voltage lag behind the input voltage by 30.0°?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven that
Input voltage Vin = 20 sin 200t
Inductance L = 400 mH
Angular frequency ω = 200 rad/sec
Inductive reactance XL = ω L = 200 × 400 × 10-3 = 80 Ω
\(V_{out}=\frac{R}{R+jX_L}\times V_{in}\)
\(V_{out}=\frac{R}{R+j80}\times V_{in}\)
The output voltage lag behind the input voltage by 30°
The phase angle of the input is 0°, so the phase angle of the output is -30° (as it is lagging).
The phase angle of the output voltage is given by
ϕ = - tan-1 (80 / R) = - 30°
⇒ (1/√3) = 80 / R
⇒ R = 138.56 ≈ 139 Ω
Last updated on Feb 24, 2025
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