(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 = f = 10 k Hz = 10 × 10³ Hz

Voltage (rms) = VrmsVrms = 120 V


To Find:

(a)
Inductive reactance at f₁ = XLXL = ?

Inductive reactance at f = XLXL = ?

(b)

Root Mean Square current at f₁ = IrmsIrms = ?

Inductive reactance at f = IrmsIrms  = ?

Solution:

(a)
The general formula for Inductive Reactance is 

XLXL 2ㄫ f L 


At Frequency f₁

XLXL 2ㄫ f₁ L

putting values

XLXL 2 × 3.1416 ×  60 Hz × 3.00 × 10⁻³ H

XLXL = 1.13 Ω --------------Ans. (1)


And at Frequency f

XLXL 2ㄫ f L

putting values

XLXL  2 × 3.1416 × 10 × 10³ Hz × 3.00 × 10⁻³ H

XLXL  = 188.4 Ω -----------------Ans. (2)


(b)
The general formula for Root Mean Square current is 

IrmsIrms VrmsXLVrmsXL

So, at frequency f₁

IrmsIrms VrmsXLVrmsXL

putting values

IrmsIrms 120V1.13Ω120V1.13Ω

IrmsIrms = 106.195 A -------------Ans.(3)


And at Frequency f₂

IrmsIrms = VrmsXLVrmsXL

putting values

IrmsIrms = 120V188.4Ω120V188.4Ω

IrmsIrms = 0.637 A -------------Ans.(4)


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