Recall and use the equation for 100% efficiency in a transformer I_p V_p = I_s V_s where p and s refer to primary and secondary

4.5.6 The Transformer

What is a Transformer?

A transformer is like a magical relay that changes the voltage of an alternating current (AC) without changing the frequency. Think of it as a power‑leveling device for electricity. 🚀

How does it work?

It uses two coils of wire (primary and secondary) wrapped around a magnetic core. When AC flows through the primary coil, it creates a magnetic field that induces a voltage in the secondary coil. The ratio of the number of turns in each coil determines the voltage change. 🔄

100 % Efficiency Equation

If a transformer were perfect (no energy lost), the power entering the primary equals the power leaving the secondary:

\$Ip Vp = Is Vs\$

Where \$Ip\$ and \$Vp\$ are the current and voltage on the primary side, and \$Is\$ and \$Vs\$ are the corresponding values on the secondary side.

Turn Ratio Example

Suppose the primary coil has 100 turns and the secondary coil has 200 turns. The turn ratio is 2:1, so the secondary voltage will be twice the primary voltage (ignoring losses). ⚡️

Exam Tip Box

Exam Tip

• Remember: For 100 % efficiency, use the equation \$Ip Vp = Is Vs\$.

• If you’re given a turn ratio, you can find the voltage ratio: \$Vs/Vp = Ns/Np\$.

• Check units: volts (V) for voltage, amperes (A) for current, watts (W) for power.

• Practice converting between primary and secondary values using the ratio.

• 💡 Tip: Think of the transformer as a “voltage‑leveling” device—just like a phone charger steps down 230 V to 5 V for your phone.

Quick Practice Questions

  1. Given \$Vp = 120\,\text{V}\$ and a turn ratio of 3:1, what is \$Vs\$? (Answer: 40 V)
  2. If \$Ip = 2\,\text{A}\$ and \$Vp = 240\,\text{V}\$, what is the power entering the primary? (Answer: 480 W)
  3. Using \$Ip Vp = Is Vs\$, if \$Is = 0.5\,\text{A}\$ and \$Vs = 10\,\text{V}\$, find \$Ip\$ when \$Vp = 200\,\text{V}\$. (Answer: 1 A)

Remember the Analogy!

Just like a water pump can change the pressure of water without changing the flow rate, a transformer changes voltage without changing frequency. 💧