1d:I[72985,["/_next/static/chunks/3th5o5azza5j1.js","/_next/static/chunks/0953gtd9gbswy.js","/_next/static/chunks/01oly6y_17ki0.js","/_next/static/chunks/1xlwfijmtjgqj.js","/_next/static/chunks/2hzca_9a7jrui.js","/_next/static/chunks/0_v6xzhg0htsf.js","/_next/static/chunks/2x0yuymt3nfdv.js","/_next/static/chunks/1hjnhv8wc11is.js"],"default"] 1e:I[63508,["/_next/static/chunks/3th5o5azza5j1.js","/_next/static/chunks/0953gtd9gbswy.js","/_next/static/chunks/01oly6y_17ki0.js","/_next/static/chunks/1xlwfijmtjgqj.js","/_next/static/chunks/2hzca_9a7jrui.js","/_next/static/chunks/0_v6xzhg0htsf.js","/_next/static/chunks/2x0yuymt3nfdv.js","/_next/static/chunks/1hjnhv8wc11is.js"],"default"] 1f:T1700,

A single-phase ideal transformer is used in the power supply unit of an industrial machine control panel. Its primary winding has $N_p = 1,000$ turns and its secondary winding has $N_s = 100$ turns. When an AC supply voltage of $V_p = 230$ V is applied across the primary winding, calculate the transformer turns ratio ( $a$ ) and the induced AC voltage across the secondary winding ( $V_s$ ). (Note: You can modify the variables in the input data section)

20:Tfae,

Click to view Transformer Classification by Turns Ratio table

Summary of winding turns, voltage, and current relationships for quick verification:

Transformer Type	Turns Condition (a = N_p / N_s)	Voltage & Current Effect	Typical Engineering Application
Step-Down Transformer	N_p > N_s (a > 1)	V_s < V_p and I_s > I_p	Utility distribution & control panel power supplies
Step-Up Transformer	N_p < N_s (a < 1)	V_s > V_p and I_s < I_p	Power plant substations for high-voltage transmission
Isolation Transformer	N_p = N_s (a = 1)	V_s = V_p and I_s = I_p	Galvanic safety isolation & noise filtering

21:T27e4,

Step 1: Calculate the transformer turns ratio ( $a$ ) (Compare the number of primary winding turns to secondary winding turns to determine the voltage transformation factor)

Step 2: Calculate the induced secondary voltage ( $V_s$ ) (By Faraday's Law of Electromagnetic Induction, the voltage across each winding is directly proportional to its number of turns)

💡 Calculator Tip: You can compute the secondary voltage in two equivalent ways: either multiply directly by the winding ratio $V_s = 230 \times \frac{100}{1000} = 23\text{ V}$ , or divide the primary voltage by the turns ratio $a$ from Step 1 ( $V_s = \frac{V_p}{a} = \frac{230}{10} = 23\text{ V}$ ). A quick sanity check to avoid accidentally inverting the fraction is that the winding with fewer turns always has the lower voltage.

22:T1e5e,

From the first step calculation, this transformer has a turns ratio ( $a$ ) of (often written on nameplates as a $10:1$ ratio), meaning every 10 turns on the primary coil correspond to 1 turn on the secondary coil. As a result, in the second step, the primary AC supply is stepped down by a factor of to an induced secondary voltage of . This makes the unit a Step-Down Transformer, which is widely used in industrial control cabinets to step 230 V mains voltage down to a safe low voltage (such as standard 24 V AC control power) for relays, contactors, and instrumentation.

In practical transformer engineering, because an ideal transformer conserves apparent power ( $V_p I_p = V_s I_s$ ), stepping the voltage down by a factor of causes the secondary current ( $I_s$ ) to increase by the exact same factor of relative to the primary current ( $I_p$ ). Consequently, when designing and manufacturing the windings, engineers must specify thicker copper wire (a larger conductor cross-sectional area) on the low-voltage secondary winding than on the high-voltage primary winding so it can carry the higher current without overheating, while also accounting for a typical 3%–5% full-load voltage drop.

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This example demonstrates how to calculate the turns ratio and induced secondary voltage of an ideal transformer, enabling engineers to properly select or design a transformer that safely steps down AC supply voltage for control circuits and electrical equipment.

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