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Chapter 28: Problem 36

For safety, medical equipment connected to patients is often powered by an isolation transformer, whose primary is connected to 120 -V AC power and whose secondary delivers \(120-\mathrm{V}\) power. What's the turns ratio of such a transformer?

Short Answer

Expert verified
The turns ratio of the transformer is 1:1.

Step by step solution

01

Understanding The Transformer's Operation

A transformer operates on the principle of magnetic induction, where an input (primary) AC voltage is converted to a different output (secondary) voltage. This conversion is done without any change to the input frequency. The key relation is \(V1/V2 = N1/N2\), where V1 and V2 are the primary and secondary voltages, and N1 and N2 are the numbers of turns in the primary and secondary, respectively. If the primary and secondary voltages are equal, which is the case in this problem, the ratio will reduce to N1/N2 = 1. It is clear from this formula that because the voltages are equal, the number of turns must also be equal.
02

Calculate The Turns Ratio

Because both the primary and secondary voltages are 120 V, the transformer must have the same number of turns in the primary and secondary coils for the voltages to be equal. Hence, the turns ratio \(N1/N2 = 1/1\). This means that for every turn in the primary coil, there is one turn in the secondary coil.
03

Conclusion

The turns ratio of a transformer with equal primary and secondary voltages is 1:1. It is important to note, however, that even though the voltages are the same, the current may not be. The current is inversely proportional to the voltage according to Ampere's Law.

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