High School

1. How many turns are in the secondary coil of a step-down transformer that reduces a voltage from 900 V to 300 V and has 15 turns in the primary coil?

2. A step-down transformer reduces voltage from 2,400 V to 120 V. What is the ratio of the number of turns in the primary coil to the number of turns in the secondary coil of the transformer?

3. The current produced by an AC generator switches direction twice for each revolution of the coil. How many times does a 110-Hz alternating current switch direction each second?

4. What is the output voltage from a step-down transformer with 200 turns in the primary coil and 100 turns in the secondary coil if the input voltage is 800 V?

5. The coil of a 60-Hz generator makes 60 revolutions each second. How many revolutions does the coil make in five minutes?

Answer :

  1. To find the number of turns in the secondary coil, we can use the transformer equation which relates the number of turns to the voltage:

[tex]\frac{V_{primary}}{V_{secondary}} = \frac{N_{primary}}{N_{secondary}}[/tex]

Given:
[tex]V_{primary} = 900[/tex] V,
[tex]V_{secondary} = 300[/tex] V,
[tex]N_{primary} = 15[/tex] turns.

Substitute these values into the equation:

[tex]\frac{900}{300} = \frac{15}{N_{secondary}}[/tex]

Simplifying the voltage ratio gives:

[tex]3 = \frac{15}{N_{secondary}}[/tex]

Cross-multiply to find:

[tex]3N_{secondary} = 15[/tex]
[tex]N_{secondary} = \frac{15}{3} = 5[/tex] turns.

  1. To find the ratio of the number of turns in the primary coil to the secondary coil, use the information provided:

[tex]V_{primary} = 2400[/tex] V,
[tex]V_{secondary} = 120[/tex] V.

The transformer equation is expressed as:

[tex]\frac{V_{primary}}{V_{secondary}} = \frac{N_{primary}}{N_{secondary}}[/tex]

Calculating the voltage ratio, we get:

[tex]\frac{2400}{120} = \frac{N_{primary}}{N_{secondary}} = 20[/tex]

Thus, the ratio of the number of turns in the primary coil to the secondary coil is 20:1.

  1. The current produced by an AC generator switches direction twice for each revolution. At 110 Hz, the generator performs 110 complete cycles per second.

Each cycle consists of two changes in direction. Therefore, the number of times the AC switches direction each second is:

[tex]2 \times 110 = 220[/tex]

  1. To find the output voltage from a step-down transformer, use the transformer equation:

[tex]\frac{V_{primary}}{V_{secondary}} = \frac{N_{primary}}{N_{secondary}}[/tex]

Given:
[tex]N_{primary} = 200[/tex],
[tex]N_{secondary} = 100[/tex],
[tex]V_{primary} = 800[/tex] V.

Substitute and solve for [tex]V_{secondary}[/tex]:

[tex]\frac{800}{V_{secondary}} = \frac{200}{100}[/tex]
[tex]\frac{800}{V_{secondary}} = 2[/tex]

Solving for [tex]V_{secondary}[/tex]:

[tex]V_{secondary} = \frac{800}{2} = 400[/tex] V.

  1. A 60-Hz generator means 60 cycles per second, and each cycle corresponds to one revolution.

Therefore, in five minutes, which is [tex]5 \times 60 = 300[/tex] seconds, the number of revolutions is:

[tex]60 \times 300 = 18000[/tex]

The coil makes 18,000 revolutions in five minutes.

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