(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) = VrmsVrms = 120 V


To Find:

(a)
Inductive reactance at f₁ = XL₁XL₁ = ?

Inductive reactance at f₂ = XL₂XL₂ = ?

(b)

Root Mean Square current at f₁ = Irms₁Irms₁ = ?

Inductive reactance at f₂ = Irms₂Irms₂  = ?

Solution:

(a)
The general formula for Inductive Reactance is 

XLXL = 2ㄫ f L 


At Frequency f₁

XL₁XL₁ = 2ㄫ f₁ L

putting values

XL₁XL₁ = 2 × 3.1416 ×  60 Hz × 3.00 × 10⁻³ H

XL₁XL₁ = 1.13 Ω --------------Ans. (1)


And at Frequency f₂

XL₂XL₂ = 2ㄫ f₂ L

putting values

XL₂XL₂  = 2 × 3.1416 × 10 × 10³ Hz × 3.00 × 10⁻³ H

XL₂XL₂  = 188.4 Ω -----------------Ans. (2)


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

IrmsIrms = VrmsXLVrmsXL

So, at frequency f₁

Irms₁Irms₁ = VrmsXL₁VrmsXL₁

putting values

Irms₁Irms₁ = 120V1.13Ω120V1.13Ω

Irms₁Irms₁ = 106.195 A -------------Ans.(3)


And at Frequency f₂

Irms₂Irms₂ = VrmsXL₂VrmsXL₂

putting values

Irms₂Irms₂ = 120V188.4Ω120V188.4Ω

Irms₂Irms₂ = 0.637 A -------------Ans.(4)


************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.