(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 Î© (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) = `\V_{rms}` = 120 V


To Find:

(a)
Inductive reactance at f₁ = `\X_L₁` = ?

Inductive reactance at f₂ = `\X_L₂` = ?

(b)

Root Mean Square current at f₁ = `\I_{rms₁}` = ?

Inductive reactance at f₂ = `\I_{rms₂}`  = ?

Solution:

(a)
The general formula for Inductive Reactance is 

`\X_L` = 2ã„« f L 


At Frequency f₁

`\X_L₁` = 2ã„« f₁ L

putting values

`\X_L₁` = 2 × 3.1416 ×  60 Hz × 3.00 × 10⁻³ H

`\X_L₁` = 1.13 Ω --------------Ans. (1)


And at Frequency f₂

`\X_L₂` = 2ã„« f₂ L

putting values

`\X_L₂`  = 2 × 3.1416 × 10 × 10³ Hz × 3.00 × 10⁻³ H

`\X_L₂`  = 188.4 Ω -----------------Ans. (2)


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

`\I_{rms}` = `\frac {V_{rms}}{X_L}`

So, at frequency f₁

`\I_{rms₁}` = `\frac {V_{rms}}{X_L₁}`

putting values

`\I_{rms₁}` = `\frac {120 V}{1.13 Ω}`

`\I_{rms₁}` = 106.195 A -------------Ans.(3)


And at Frequency f₂

`\I_{rms₂}` = `\frac {V_{rms}}{X_L₂}`

putting values

`\I_{rms₂}` = `\frac {120 V}{188.4 Ω}`

`\I_{rms₂}` = 0.637 A -------------Ans.(4)


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