A series circuit has a 0.25 henry inductor, a 340 ohm resistor, and a 0.000009 farad capacitor. There is an initial charge of 0.000004 coulombs, there is no initial current, and there is an applied voltage which is described as . Identify the amplitude of the steady-state solution.
A) 0.000003
B) 0.000009
C) 0.35
D) 0.175

Question

A series circuit has a 0.25 henry inductor, a 340 ohm resistor, and a 0.000009 farad capacitor. There is an initial charge of 0.000004 coulombs, there is no initial current, and there is an applied voltage which is described as  . Identify the amplitude of the steady-state solution.
A) 0.000003 
B) 0.000009 
C) 0.35 
D) 0.175

Quizplus · Accepted Answer

Using the given values, we can calculate the resonant frequency of the circuit as:
f = 1 / (2π√(LC)) = 1 / (2π√(0.25*0.000009)) ≈ 1322.87 Hz.

Next, we can calculate the impedance of the circuit at this frequency as:
Z = R + j(XL - XC) = 340 + j(2πfL - 1/(2πfC))
= 340 + j(2π*1322.87*0.25 - 1/(2π*1322.87*0.000009))
≈ 340 + j1725.87 - j555.36

The amplitude of the steady-state solution can be found by dividing the initial charge by the magnitude of the impedance:
|Vss| = |Q / Z| = |0.000004 / (340 + j1170.51)| ≈ 0.000009.

Therefore, the correct choice is B.

A Series Circuit Has a 0