All three circuits shown below have R = 100 Ω, L = 0.1 H and emf ε = (5.0 V) sin (377 t). Which statement regarding the angular resonance frequencies ωA, ωB, and ωC is correct? A)ωC ωA = ωB B)ωC

Question

All three circuits shown below have R = 100 Ω, L = 0.1 H and emf ε = (5.0 V) sin (377 t). Which statement regarding the angular resonance frequencies ωA, ωB, and ωC is correct? A)ωC > ωA = ωB B)ωC < ωA = ωB C)ωA = ωB = ωC D)ωB < ωA = ωC E)ωB > ωA = ωC

Quizplus · Accepted Answer

The angular resonance frequency for an RLC circuit is given by ω = 1/√(LC)
For all three circuits, L = 0.1 H and R = 100 Ω. Therefore, the angular resonance frequency for each circuit is: 
ω = 1/√(LC) = 1/√(0.1*100) = 1/√10 = √10/10 = 0.316 rad/s
Thus, ωA, ωB, and ωC are all equal to 0.316 rad/s. Therefore, the correct statement regarding the angular resonance frequencies is that ωA = ωB = ωC.

All Three Circuits Shown Below Have R = 100 Ω