Question

What is the inductive reactance of a coil of inductance 10mH at a frequency

1.  50 Hz
2. 1000 Hz
3. 20 kHz?

Answer 1

Given: L = 10 mH = 10 × 10^-3 H = 10^–2 H,
f₁ = 50 Hz,
f₂ = 1000 Hz,
f₃ = 20 kHz = 20000 Hz   

To find:

1. The reactance of the coil at 50 Hz (X_L)₁
2. The reactance of the coil at 1000 Hz (X_L)₂
3. Reactance of the coil at 20 kHz (X_L)₃

Formula: XL = 2πfL  

Calculation:

(i) Using formula,  

(X_L)₁ = 2πf₁L = 2 × 3.14 × 50 × 10^–2 

(X_L)₁ = 3.14 Ω

(ii) Using formula,  

(X_L)₂ = 2πf₂L = 2 × 3.14 × 1000 × 10^–2 

(X_L)₂ = 62.8 Ω

(iii) Using formula,  

(X_L)₃ = 2πf₃L = 2 × 3.14 × 20000 × 10^–2 

(X_L)₃ = 1256 Ω