Question

Figure 31-24 shows three situations like those in Fig. 31-15. Is the driving angular frequency greater than, less than, or equal to the resonant angular frequency of the circuit in (a) situation 1, (b) situation 2, and (c)situation 3?

Short answer

1. The angular frequency in situation 1 is less than the resonant angular frequency of the circuit.
2. The angular frequency in situation 2 is equal to the resonant angular frequency of the circuit.
3. The angular frequency in situation 3 is greater than the resonant angular frequency of the circuit.

Step-by-step solution

The given data

Figure 31-24 shows three situations of frequencies.

Understanding the concept of resonance frequency

When the current leads the emf, then the angular frequency is less and vice versa. This case of current leading indicates flowing through a capacitor. If current lags the emf, this is when the current flows through an inductor.

a) Calculation of the angular frequency in situation 1

The current I leads the driving emf E, so angular frequency is less than the resonant frequency.

b) Calculation of the angular frequency in situation 2

The current I and the driving emf E have the same phase difference, so angular frequency is equal to the resonant frequency.

c) Calculation of the angular frequency in situation 3

The current I is larger than the driving emf E, so the angular frequency is greater than the resonant frequency.