A step-down transformer installed in an industrial power supply has 1{}200\text{ turns} on… — Armed Services Vocational Aptitude Battery (ASVAB)

A step-down transformer installed in an industrial power supply has $1{}200\text{ turns}$ on its primary winding and $300\text{ turns}$ on its secondary winding. If the secondary coil delivers a current of $8\text{ A}$ to an operating load, what is the primary current ( $I_p$ ) drawn from the alternating current ( $\text{AC}$ ) source?

A
$32\text{ A}$
$2\text{ A}$ Answer
C
$0.5\text{ A}$
D
$200\text{ mA}$

Answer

The primary current drawn from the source is

2\text{ A}

In an ideal transformer, input power equals output power (

V_p \times I_p = V_s \times I_s

). Therefore, current is inversely proportional to the turns ratio:

\frac{I_p}{I_s} = \frac{N_s}{N_p}

. With a

4:1

step-down turns ratio (

1{}200\text{ turns}

300\text{ turns}

), the secondary current of

8\text{ A}

corresponds to a primary current of

8\text{ A} \div 4 = 2\text{ A}

Step-by-Step Solution

Calculate the turns ratio of the transformer (

N_p / N_s

\text{Turns Ratio} = \frac{N_p}{N_s} = \frac{1{}200}{300} = 4

The turns ratio defines the proportional relationship between primary and secondary electrical parameters.

Apply the inverse current relationship for an ideal transformer (

I_p / I_s = N_s / N_p

I_p = I_s \times \left(\frac{N_s}{N_p}\right) = 8\text{ A} \times \left(\frac{300}{1{}200}\right) = 8\text{ A} \times \frac{1}{4} = 2\text{ A}

Because transformers conserve power (

P_{\text{in}} = P_{\text{out}}

), stepping down voltage by a factor of 4 causes current to step up by a factor of 4, meaning the primary current must be one-fourth of the secondary current.

Key Concept

Transformer Current and Turns Relationship

Estimated Time:1m 0s

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