A 100 μH coil has a Q value of 200 at 2 MHz. The effective resistance of the coil is ________.

Concept:

The quality factor is the ratio of reactance and resistance. You can calculate the effective resistance R and effective reactance X of the RLC circuit for a given frequency. 

Q = X/R = ωL/R

Where;

ω → Angular frequency 

R→ Effective resistance

Calculation:

Given;

L = 100 μH

f = 2 Mhz

Q= 200

Then

    Q = ωL/R

⇒ R = ωL/Q

∴ R = 2πfL/Q = (2π × 2 × 10⁶ ×100 × 10^-6)/200 = 2π Ω