A 25.0-mH inductor,a 2.00-μF capacitor,and a certain resistor are connected in series across an ac voltage source at 1000 Hz.If the impedance of this circuit is 200 Ω,what is the resistance of the resistor?
A) 100 Ω
B) 184 Ω
C) 200 Ω
D) 552 Ω
E) 579 Ω

Question

Quizplus · Accepted Answer

The impedance of the circuit is given by:

Z = √(R^2+(ωL-1/(ωC))^2)

where 
R is the resistance of the resistor
L is the inductance of the inductor 
C is the capacitance of the capacitor
ω = 2πƒ is the angular frequency

Substituting the given values, we get:

200 = √(R^2+(2π×1000×25×10^-3-1/(2π×1000×2×10^-6))^2)

Simplifying and solving for R, we get:

R = 184 Ω

Therefore, the option B is correct.

A 250-MH Inductor,a 2