Question

Ch 31 HW Problem 31.63 10 of 15 Constants In an L-R-C series circuit, the source has a voltage amplitude of 116 V , R = 77.0 Ω , and the reactance of the capacitor is 473 Ω . The voltage amplitude across the capacitor is 364 V . Part A What is the current amplitude in the circuit? II = nothing A Request Answer Part B What is the impedance? ZZ = nothing Ω Request Answer Part C What two values can the reactance of the inductor have? Enter your answers in ascending order separated by a comma. XLX L = nothing Ω Request Answer Part D For which of the two values found in part (c) is the angular frequency less than the resonance angular frequency? For which of the two values found in part (c) is the angular frequency less than the resonance angular frequency? the less value of XL the larger value of XL Request Answer Provide Feedback

Answer 1

Answer:

a. I = 0.76 A

b. Z = 150.74

c. RL₁ = 34.41  ,  RL₂ = 602.58

d. RL₂ = 602.58

Explanation:

V₁ = 116 V , R₁ = 77.0 Ω , Vc = 364 V ,  Rc = 473 Ω

a.

Using law of Ohm

V = I * R

I = Vc / Rc =  364 V / 473 Ω

I = 0.76 A

b.

The impedance of the circuit in this case the resistance, capacitance and inductor

V = I * Z

Z = V / I

Z = 116 v / 0.76 A

Z = 150.74

c.

The reactance of the inductor can be find using

Z² = R² + (RL² - Rc²)

Solve to RL'

RL = Rc (+ / -) √ ( Z² - R²)

RL = 473 (+ / -)  √ 150.74² 77.0²

RL = 473 (+ / -)  (129.58)

RL₁ = 34.41  ,  RL₂ = 602.58

d.

The higher value have the less angular frequency  

RL₂ = 602.58

ω = 1 / √L*C

ω = 1 / √ 602.58 * 473

f = 285.02 Hz