Question

An RL circuit contains a resistor with R = 6800 Ω and an inductor with L = 2300 µH. If the impedance of this circuit is 160,000 Ω, what is the frequency?

_______Hz

Answer 1

| Impedance | = √ [R² +(ωL)²]

R² = 6800² = 4.624 x 10⁷

(ωL)² = (2 · π · f · 2.3 · 10⁻³)²

= 2.0884 x 10⁻⁴ f²

| Z | = √[ (4.624 x 10⁷) + (2.0884 x 10⁻⁴ f²) ] = 1.6 x 10⁵

(1.6 x 10⁵)² = (4.624 x 10⁷) + (2.0884 x 10⁻⁴ f²)

(2.56 x 10¹⁰) - (4.624 x 10⁷) = 2.0884 x 10⁻⁴ f²


Frequency² = (2.56 x 10¹⁰ - 4.624 x 10⁷) / 2.0884 x 10⁻⁴

= 2.555 x 10¹⁰ / 2.0884 x 10⁻⁴

= 1.224 x 10¹⁴

= 122,400 GHz <== my calculation

11.1 MHz <== online impedance calculator

Obviously, I must have picked up some rounding errors
in the course of my calculation.