A technician connects a step-up transformer to a 30\text{ V} AC power supply. The transfor… — Armed Services Vocational Aptitude Battery (ASVAB)

A technician connects a step-up transformer to a $30\text{ V}$ AC power supply. The transformer has $200\text{ turns}$ on its primary winding and $800\text{ turns}$ on its secondary winding. Assuming ideal operating conditions with no energy losses, what is the output voltage at the secondary winding?

A
$7.5\text{ V}$
B
$12\text{ V}$
$120\text{ V}$ Answer
D
$0\text{ V}$

Answer

The secondary output voltage is

120\text{ V}

For an ideal transformer, secondary voltage is calculated using the formula

V_s = V_p \times \left(\frac{N_s}{N_p}\right)

. Given a primary voltage of

30\text{ V}

and a turns ratio of

\frac{800}{200} = 4

, the secondary voltage is

30\text{ V} \times 4 = 120\text{ V}

Step-by-Step Solution

Identify the known values and the transformer voltage-turns relationship formula.

V_p = 30\text{ V}

N_p = 200\text{ turns}

N_s = 800\text{ turns}

, using

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

In an ideal transformer, the ratio of the secondary voltage to the primary voltage equals the ratio of secondary turns to primary turns.

Calculate the turns ratio (

N_s / N_p

\frac{800}{200} = 4

Finding the ratio simplifies multiplying the primary voltage to determine secondary voltage.

Multiply the primary input voltage by the turns ratio to find the secondary voltage (

V_s

V_s = 30\text{ V} \times 4 = 120\text{ V}

Since the secondary winding has four times as many turns as the primary, the secondary voltage must be four times greater than the primary voltage.

Key Concept

Transformer Turns and Voltage Ratio

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