32.5 The Series RLC Circuit 917 like to oscillate. Consequently, the circuit has

Question

32.5 The Series RLC Circuit 917 like to oscillate. Consequently, the circuit has a large current response when the FIGURE 32.18 A graph of the current ! oscillating emf matches this frequency versus emf frequency for a series RLC FIGURE 32.18 shows the peak current Iof a series RLC circuit as the emf frequency is varied. Notice how the current increases until reaching a maximum at frequency The maximum current is ER then decreases. This is the hallmark of a resonance -851 As R decreases, causing the damping to decrease, the maximum current becomes larger and the curve in Figure 32.18 becomes narrower. You saw exactly the same behavior for a driven mechanical oscillator. The emf frequency must be very close to l in order for a lightly damped system to respond, but the response at resonance is very large For a different perspective. FIGURE 32.1, graphs the instantaneous emf E &cosar; and current i = /cos(or-4) for frequencies below. at. and above ob-The current and the emf are in phase at resonance ( = 0 rad) because the capacitor and inductor essentially cancel each other to give a purely resistive circuit. Away from resonance the current decreases and begins to get out of phase with the emf. You can see, from Equation 32.27. that the phase angle is negative when x.1000 kHz is the emf. 0.28 mA VISUALIZE The circuit looks like Figure 32.16. SOLVE a. The capacitor needs to be tuned to where it and the inductor are resonant at o2m x 1000 kHz. The ASSESS These are realistic values for the imput stage of an AM radio. You can see that the signal from the 1050 kHz station is strongly suppressed when the radio is tuned to 1000 kHz appropriate value is

Explanation / Answer

1.

The resonance occurs for particular frequency().

2.

At the resonance phase angle =0

3.

Phase angle is positive when XL > Xc and Phase angle is negative when XL < Xc where

XL is Inductive reactance Xc is capacitive reactance

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