Answer to Question 9

 

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A loudspeaker has an inductance of 1.25 10-4 H and a resistance of 4.0 W. It is connected in series with an inductor of inductance 3.0 10-5 H and resistance 1.0 W. A frequency of 1400 Hz is passed through the loudspeaker. Calculate:
(a) the reactance of each of the components;
(b) the combined impedance at this frequency.
 

Model the speaker and the low pass filter as two inductors in series and two resistors in series.

(a) Speaker:  XL = 2p 1400 Hz 1.25 10-4 Hz  = 1.10 W

     Inductor:  XL = 2p 1400 Hz 3.0 10-5 Hz  = 0.264 W

 

(b)  Total inductance = 1.10 W + 0.264 W = 1.36 W

       Total resistance = 4.0 W + 1.0 W = 5.0 W

     Impedance:

      Z2 = (5.0 W)2 + (1.36 W)2 = 26.86 W2

      Z = 5.2 W (2 s.f.)