In Fig. 31-35, let the rectangular box on the left represent the (high-impedance) output of an audio amplifier, with . Let represent the (low-impedance) coil of a loudspeaker. For maximum transfer of energy to the load we must have , and that is not true in this case. However, a transformer can be used to “transform” resistances, making them behave electrically as if they were larger or smaller than they actually are. (a) Sketch the primary and secondary coils of a transformer that can be introduced between the amplifier and the speaker in Fig. 31-35 to match the impedances. (b) What must be the turns ratio?
(a) Sketch the primary and secondary coils.
(b) Turns ratio is 10.
The resistance ,
The resistance ,
A transformer is a device that transfers electrical energy from one alternating current circuit to one or more other circuits by either increasing (stepping up) or decreasing (stepping down) the voltage.
Use the relation between primary current, the number of turns in the primary coil, secondary current, and the number of turns in the secondary coil.
Then by using the formula for power,define the ratio of turns.
The RMS current in secondary coil is as follows
The primary current in circuit is given as,
Then power equation is written as follows.
Then differentiate with respect to :
But we know
Hence, number of turns ratio is 10.
An alternating emf source with a certain emf amplitude is connected, in turn, to a resistor, a capacitor, and then an inductor. Once connected to one of the devices, the driving frequency is varied and the amplitude of the resulting current through the device is measured and plotted. Which of the three plots in Fig. 31-22 corresponds to which of the three devices?
An inductor is connected across a capacitor whose capacitance can be varied by turning a knob. We wish to make the frequency of oscillation of this LC circuit vary linearly with the angle of rotation of the knob, going from as the knob turns through 180°. If , plot the required capacitance C as a function of the angle of rotation of the knob.
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