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Suppose that an ideal transformer has 400 turns in its primary coil and 100 turns in its secondary coil. The primary coil is connected to a 120 V (rms) electric outlet and carries an rms current of 10 mA. What are the rms values of the voltage and current for the secondary?

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cjmejiab

To solve this problem we need to use the induced voltage ratio law with respect to the number of turns in a solenoid. So

[tex]\frac{\epsilon_2}{\epsilon_1} = -\frac{N_2}{N_1}[/tex]

For the given values we have to

[tex]N_1 = 400[/tex]

[tex]N_2 = 100[/tex]

[tex]\epsilon_2 = 120V[/tex]

Replacing we have that,

[tex]\frac{\epsilon_2}{120} = -\frac{100}{400}[/tex]

[tex]\epsilon = 30V[/tex]

Therefore the RMS value for secondary is 30V.

The current can be calculated at the same way, but here are inversely proportional then,

[tex]\frac{I_2}{I_1} = -\frac{N_1}{N_2}[/tex]

Replacing we have

[tex]\frac{I_2}{10mA} = -\frac{400}{100}[/tex]

[tex]I_2 = 40mA[/tex]

Therefore the rms value of current for secondary is 40mA

Lanuel

The rms values of the voltage and current for the secondary coil is equal to 30 Volts and 40 mA respectively.

Given the following data:

  • Number of turns in primary coil = 400 turns
  • Number of turns in secondary coil = 100 turns
  • Electromotive force (emf) in primary coil = 120 Volt (rms)
  • Current in primary coil = 10 mA (rms)

To determine the rms values of the voltage and current for the secondary coil:

For the voltage:

Since the transformer is an ideal transformer, we would apply the voltage transformer ratio.

Mathematically, voltage transformer ratio is given by this formula:

[tex]\frac{E_1}{N_1} = \frac{E_2}{N_2}[/tex]

Where:

  • [tex]E_1[/tex] is the emf in the primary coil.
  • [tex]E_2[/tex] is the emf in the secondary coil.
  • [tex]N_2[/tex] is the number of turns in secondary coil.
  • [tex]N_1[/tex] is the number of turns in primary coil.

Substituting the given parameters into the formula, we have;

[tex]\frac{120}{400} = \frac{E_2}{100}\\\\120 \times 100 = 400E_2\\\\E_2 = \frac{12000}{400} \\\\E_2 = 30 \; Volts\; (rms)[/tex]

For the current:

[tex]\frac{I_2}{I_1} = \frac{N_1}{N_2} \\\\\frac{I_2}{10} = \frac{400}{100} \\\\\frac{I_2}{10} = 4\\\\I_2 = 40 \; mA[/tex] (rms)

Read more: https://brainly.com/question/14937588

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