(a) Calculate the inductive reactance of a 3.00 mH inductor, when 60.0 Hz and 10.0 kHz AC voltages are applied. (b) What is the RMS current at each frequency if the applied RMS voltage is 120 V? Ans ((a) 1.13 Ω, 188 Ω (b) 106 A, 0.637 A)
Data Given:
Inductance of an inductor = L = 3.00 mH = 3.00 × 10⁻³ H
1st value of Frequency = f₁ = 60 Hz
2nd value of Frequency = f₂ = 10 k Hz = 10 × 10³ Hz
Voltage (rms) = Vrms = 120 V
To Find:
(a)
Inductive reactance at f₁ = XL₁ = ?
Inductive reactance at f₂ = XL₂ = ?
(b)
Root Mean Square current at f₁ = Irms₁ = ?
Inductive reactance at f₂ = Irms₂ = ?
Solution:
(a)
The general formula for Inductive Reactance is
XL = 2ㄫ f L
At Frequency f₁
XL₁ = 2ㄫ f₁ L
putting values
XL₁ = 2 × 3.1416 × 60 Hz × 3.00 × 10⁻³ H
XL₁ = 1.13 Ω --------------Ans. (1)
And at Frequency f₂
XL₂ = 2ㄫ f₂ L
putting values
XL₂ = 2 × 3.1416 × 10 × 10³ Hz × 3.00 × 10⁻³ H
XL₂ = 188.4 Ω -----------------Ans. (2)
(b)
The general formula for Root Mean Square current is
Irms = VrmsXL
So, at frequency f₁
Irms₁ = VrmsXL₁
putting values
Irms₁ = 120V1.13Ω
Irms₁ = 106.195 A -------------Ans.(3)
And at Frequency f₂
Irms₂ = VrmsXL₂
putting values
Irms₂ = 120V188.4Ω
Irms₂ = 0.637 A -------------Ans.(4)
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