An auxiliary power transformer on a vessel steps down an input voltage of 440\text{ V AC} … — Armed Services Vocational Aptitude Battery (ASVAB)

An auxiliary power transformer on a vessel steps down an input voltage of $440\text{ V AC}$ to $110\text{ V AC}$ . If the secondary winding is connected to a lighting circuit drawing $14\text{ A}$ , what is the primary current in amperes ( $\text{A}$ ), assuming an ideal transformer with zero power losses?

Cevap: 3.5 A

Cevap

The primary current is

3.5\text{ A}

In an ideal transformer with negligible losses, the primary apparent power equals the secondary apparent power (

V_p \times I_p = V_s \times I_s

). Because the transformer reduces voltage from

440\text{ V AC}

110\text{ V AC}

4:1

step-down ratio), the primary winding requires only one-fourth of the secondary current. Multiplying

14\text{ A}

\frac{110}{440}

yields

3.5\text{ A}

Adım Adım Çözüm

State the ideal transformer power balance equation

V_p \times I_p = V_s \times I_s

An ideal transformer operates at 100% efficiency, meaning input power (

P_p

) equals output power (

P_s

Isolate the unknown primary current variable (

I_p

)

I_p = I_s \times \left(\frac{V_s}{V_p}\right)

Dividing both sides by the primary voltage (

V_p

) provides the direct formula for primary current.

Substitute the given numerical values and calculate

I_p = 14\text{ A} \times \left(\frac{110\text{ V}}{440\text{ V}}\right) = 14 \times \frac{1}{4} = 3.5\text{ A}

The voltage is stepped down by a factor of

4

, which requires the current to be stepped down by the inverse factor of

4

in the primary circuit relative to the secondary.

Anahtar Kavram

Transformer Voltage and Current Transformation Ratio

Tahmini Süre:1m 0s

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