Chapter 32, Problem 47AP

You are trying to become a member of the Physics Olympics team. Your physics professor is training you and some other students by having you compete with each other to solve problems as accurately and quickly as you can. During one session, he springs the RLC circuit shown in Figure P32.47 (page 872) on you. Figure P32.47a shows the circuit with a battery as the energy source. The battery has an emf $\mathcal{E}$ and internal resistance r. He tells you the following, assuming switch S has been at position a for a long time:

• If only switch S_L is closed, and switches S_C and S_R are open, and then switch S is thrown to position b, the time constant of the circuit is τ₁ = 0.200 ms. Switch S is returned to position a for a long time.

Figure P32.47

• If only switch S_C is closed, and switches S_L and S_R are open, and then switch S is thrown to position b, the time constant of the circuit is τ₂ = 0.050 0 ms. Switch S is returned to position a for a long time.

In Figure P32.47b, an AC source with a variable frequency has been added to the same circuit, and switch S is thrown to position b. Switches S_C, S_L, and S_R are all open. At what angular frequency ω should the AC source be set so that the circuit exhibits resonance? Quick! Get to work!