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Difficulty: MediumInductors and Transformers

An AC step-down transformer has 600 turns600\text{ turns} on its primary winding and 50 turns50\text{ turns} on its secondary winding. The primary winding is connected to a 120 V120\text{ V} AC source, and the secondary circuit delivers current to a load drawing 2.4 A2.4\text{ A}. What is the current flowing in the primary winding?

  1. A
    28.8 A28.8\text{ A}
  2. B
    20 mA20\text{ mA}
  3. 0.2 A0.2\text{ A}Answer
  4. D
    0 A0\text{ A}

Answer

0.2 A0.2\text{ A}
In an ideal transformer, the ratio of primary current to secondary current is inversely proportional to the ratio of primary turns to secondary turns (Ip/Is=Ns/NpI_p / I_s = N_s / N_p). Since the transformer has a 12:112:1 step-down turns ratio (600/50=12600/50 = 12), the secondary voltage decreases by a factor of 12 while the primary current must be 12 times smaller than the secondary current: Ip=2.4 A/12=0.2 AI_p = 2.4\text{ A} / 12 = 0.2\text{ A}.

Step-by-Step Solution

1
Determine the turns ratio between the primary and secondary windings
NpNs=60050=12\frac{N_p}{N_s} = \frac{600}{50} = 12
The turns ratio determines both the voltage transformation ratio and the inverse current transformation ratio.
2
Apply the transformer current relationship to solve for primary current (IpI_p)
IpIs=NsNp  ⟹  Ip=2.4 A×50600=2.4 A12=0.2 A\frac{I_p}{I_s} = \frac{N_s}{N_p} \implies I_p = 2.4\text{ A} \times \frac{50}{600} = \frac{2.4\text{ A}}{12} = 0.2\text{ A}
In an ideal transformer, power in equals power out (VpIp=VsIsV_p I_p = V_s I_s), which means current is inversely proportional to the number of turns.

Key Concept

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

Inductors and Transformers

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