In an electronic power system, two ideal transformers are cascaded (connected in sequence)… — Armed Services Vocational Aptitude Battery (ASVAB)

In an electronic power system, two ideal transformers are cascaded (connected in sequence).

Transformer 1 receives an input voltage of $1{}200\text{ V AC}$ on its primary coil, which has $3{}000\text{ turns}$ . The secondary coil of Transformer 1 has $600\text{ turns}$ , and its output voltage is fed directly into the primary coil of Transformer 2.

Transformer 2 further steps down this voltage to supply exactly $48\text{ V AC}$ to an electronic load.

If the secondary coil of Transformer 2 contains $50\text{ turns}$ , how many turns must the primary coil of Transformer 2 have?

Cevap: 250 turns

Cevap

250 turns

The correct answer is derived by sequentially applying the transformer turns ratio formula (

V_p/V_s = N_p/N_s

) across the cascaded system. Transformer 1 operates with a 5:1 step-down ratio, reducing the

1{}200\text{ V}

input to

240\text{ V}

. Transformer 2 receives this

240\text{ V}

and must further step it down to

48\text{ V}

, which also requires a 5:1 ratio. Multiplying the

50

secondary turns by this ratio yields

250

primary turns.

Adım Adım Çözüm

Calculate the secondary voltage of Transformer 1.

V_{s1} = 240\text{ V AC}

Using the turns ratio formula

V_{s1} / V_{p1} = N_{s1} / N_{p1}

, we find

V_{s1} = 1{}200 \times (600 / 3{}000) = 1{}200 \times 0.2 = 240\text{ V AC}

Identify the primary voltage of Transformer 2.

V_{p2} = 240\text{ V AC}

Because the transformers are cascaded in series, the output voltage of Transformer 1 serves directly as the input voltage for Transformer 2.

Set up the turns ratio equation for Transformer 2.

N_{p2} / 50 = 240 / 48

Applying the turns ratio formula

N_{p2} / N_{s2} = V_{p2} / V_{s2}

to the second transformer using its specific input and output voltages.

Solve for the primary turns of Transformer 2.

N_{p2} = 250\text{ turns}

N_{p2} = 50 \times (240 / 48) = 50 \times 5 = 250\text{ turns}

Anahtar Kavram

Cascaded Transformer Turns Ratios

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Cevap

Adım Adım Çözüm

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