What are the values of circuit constants?

Question

In a particular R-L series circuit a voltage of 10V at 50 Hz produces a current of 700mA while the same
voltage at 75 Hz produces 500 mA. What are the values of circuit constants?

Answer 1

(i) Z = √(R² + (2π x 50L)²) = √(R² + 98696L²);

V = IZ or 10 = 700 x 10^-3√(R² + 98696L²)

√(R² + 98696L²) = 10/700  × 10⁻³ = 100/7 

or R² + 98696 L² = 10000/49 ...(i)

(ii) In the second case Z = √(R² + (2π x 75L)²) = √(R² + 222066L²)

∴ 10 = 500 x 10^-3√(R² + 222066L²) i.e √(R² + 222066L²) = 20 or R² + 222066L² = 400 (ii)

Subtracting Eq. (i) from (ii), we get 

222066 L² − 98696 L² = 400 − (10000/49) or 123370 L² = 196 

or L = 0.0398 H = 40 mH. 

Substituting this value of L in Eq. (ii), we get, R² + 222066 (0.398)² = 400 

∴ R = 6.9 Ω