A power adapter uses a step-down transformer with 400\text{ turns} on the primary coil and… — Armed Services Vocational Aptitude Battery (ASVAB)

A power adapter uses a step-down transformer with $400\text{ turns}$ on the primary coil and $20\text{ turns}$ on the secondary coil. If an input voltage of $120\text{ V AC}$ is applied across the primary coil, what is the secondary output voltage in volts?

Answer: 6 V

Answer

The secondary output voltage is

6\text{ V}

In a transformer, the ratio of secondary voltage to primary voltage equals the ratio of secondary turns to primary turns (

V_s / V_p = N_s / N_p

). With

400

primary turns and

20

secondary turns, the turns ratio is

20 / 400 = 1/20

. Multiplying the primary voltage (

120\text{ V}

) by

1/20

yields a secondary output voltage of

6\text{ V}

Step-by-Step Solution

Identify the given transformer parameters from the problem statement.

V_p = 120\text{ V}

N_p = 400\text{ turns}

, and

N_s = 20\text{ turns}

These parameters are required to determine the relationship between primary and secondary voltages.

Set up the transformer turns ratio equation relating primary and secondary voltages to coil turns.

\frac{V_s}{V_p} = \frac{N_s}{N_p}

The voltage induced across a transformer winding is directly proportional to the number of turns in that winding.

Substitute the known values into the equation and compute the secondary voltage

V_s

V_s = 120\text{ V} \times \left(\frac{20}{400}\right) = 120\text{ V} \times 0.05 = 6\text{ V}

Direct algebraic calculation yields the step-down output voltage.

Key Concept

Transformer Turns Ratio and Voltage Transformation

Estimated Time:45s

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