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Difficulty: MediumInductors and Transformers

A step-up transformer utilized in an industrial ignition system has 80 turns80\text{ turns} on its primary coil and 1200 turns1{}200\text{ turns} on its secondary coil. When the primary coil is energized by a 16 V AC16\text{ V AC} source, the secondary circuit delivers a current of 40 mA40\text{ mA} to its load. Assuming an ideal transformer, what is the current drawn by the primary coil?

  1. A
    2.67 mA2.67\text{ mA}
  2. 600 mA600\text{ mA}Answer
  3. C
    0.6 mA0.6\text{ mA}
  4. D
    40 mA40\text{ mA}

Answer

600 mA600\text{ mA}
In an ideal transformer, power is conserved (Pp=PsP_p = P_s), which means voltage and current vary inversely with the turns ratio. For this transformer, the secondary-to-primary turns ratio is 120080=15\frac{1{}200}{80} = 15. While voltage steps up by a factor of 15, current steps down by a factor of 15. Therefore, the primary current must be 15 times the secondary current: Ip=40 mA×15=600 mAI_p = 40\text{ mA} \times 15 = 600\text{ mA} (or 0.6 A0.6\text{ A}).

Step-by-Step Solution

1
Calculate the turns ratio of the transformer
Turns ratio NsNp=120080=15\frac{N_s}{N_p} = \frac{1{}200}{80} = 15
The turns ratio establishes how voltage and current scale between the primary and secondary windings.
2
Apply the inverse current transformation formula for ideal transformers
Ip=Is×(NsNp)=40 mA×15=600 mAI_p = I_s \times \left(\frac{N_s}{N_p}\right) = 40\text{ mA} \times 15 = 600\text{ mA}
Because transformers conserve power (VpIp=VsIsV_p I_p = V_s I_s), a step-up in voltage results in a proportional step-down in current, meaning the primary current must be greater than the secondary current by the turns ratio.

Key Concept

Transformer Current and Turns Ratio Relationship
Estimated Time:1m 0s
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Topics

Inductors and Transformers

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