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Fundamentals Of Physics
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Short Answer

In Fig. 31-35, let the rectangular box on the left represent the (high-impedance) output of an audio amplifier, with r=1000 ohm . Let R=10 ohm represent the (low-impedance) coil of a loudspeaker. For maximum transfer of energy to the load R we must have R = r , 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.

See the step by step solution

Step by Step Solution

Step 1: Listing the given quantities

The resistance r=1000 ohm,

The resistance R=10 ohm,

Step 2: Understanding the concepts of transformer

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.

Formula:

Is=NpIpNs

P=Is2 R

Ip=εrmsReq+r

Step 3: (a)Sketch of the primary and secondary coils:

Step 4: (b) Calculations of the turn’s ratio:

The RMS current in secondary coil is as follows

Is=NpIpNs

The primary current in circuit is given as,

Ip=εrmsReq+r=εrmsNpNs2R+r

Then power equation is written as follows.

P=εrmsNpNs2R+r2NpNs2R

Let’s assume

x=NpNs2

Pavg=εrms2×R×xxR+r2

Then differentiate with respect to x:

dPavgdx=εrms2×R×r-xRxR+r3=0

εrms2×R×r-xRxR+r3=0

So,

x=rR=100010=100 ohm

But we know

x=NpNs2NpNs2=100NpNs=10

Hence, number of turns ratio is 10.

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