7.8 Transformers ⚡

1 Why bother with transformers?

A transformer lets us raise or lower an alternating-current (ac) voltage without changing its frequency. Need a tiny charger for your phone or a giant grid-level boost? A transformer handles both jobs thanks to mutual induction—a changing magnetic field in one coil creates an emf in another. 🔄 :contentReference[oaicite:0]{index=0}

2 Basic build 🛠️

  • Two separate coils wound on the same soft-iron core keep the magnetic flux locked in. You can wind the coils one over the other or place them on separate limbs of a laminated core. :contentReference[oaicite:1]{index=1}
  • Primary coil: Np turns (input side).
    Secondary coil: Ns turns (output side).

3 How the maths tells the story 📐

When you apply an ac voltage vp to the primary, the changing flux φ in the core induces emfs:

  • Secondary emf: \( \varepsilon_s = -N_s \dfrac{d\phi}{dt} \) :contentReference[oaicite:2]{index=2}
  • Primary back-emf: \( \varepsilon_p = -N_p \dfrac{d\phi}{dt} \) :contentReference[oaicite:3]{index=3}

For normal operation \( \varepsilon_p = v_p \) and (with light secondary load) \( \varepsilon_s = v_s \). Dividing the two gives the turns–voltage ratio: \[ \frac{v_s}{v_p} = \frac{N_s}{N_p}. \] :contentReference[oaicite:4]{index=4}

Assuming ideal (100 % efficient) behaviour, power in equals power out: \[ i_p v_p = i_s v_s, \] :contentReference[oaicite:5]{index=5} so \[ \frac{i_s}{i_p} = \frac{N_p}{N_s}. \] :contentReference[oaicite:6]{index=6}

Step-up vs. step-down 🔼🔽

Using the ratios above:

  • Step-up (boost the voltage): Ns > Np ⇒ Vs > Vp but Is < Ip. Example: 100 turns → 200 turns turns 220 V @ 10 A into 440 V @ 5 A. 🚀 :contentReference[oaicite:7]{index=7}
  • Step-down (lower the voltage): Ns < Np ⇒ Vs < Vp but Is > Ip. 🔋 :contentReference[oaicite:8]{index=8}

4 Why real transformers aren’t perfect 🤔

Even the best units hit about 95 % efficiency. Key energy losses include:

  1. Flux leakage: Some magnetic flux misses the secondary. Minimise it by tightly inter-winding the coils. :contentReference[oaicite:9]{index=9}
  2. Wire resistance: I2R heating in the coils. Thicker wire helps, especially on low-voltage, high-current windings. :contentReference[oaicite:10]{index=10}
  3. Eddy currents in the iron core: Laminating the core breaks up these swirling currents and cuts heating. :contentReference[oaicite:11]{index=11}
  4. Hysteresis loss: Magnetisation flips each cycle and wastes energy as heat. Use a soft magnetic alloy with a narrow hysteresis loop. :contentReference[oaicite:12]{index=12}

5 Big-picture use 🌍

Power plants crank out thousands of volts. A step-up transformer sends that power down long lines with small current, slashing I2R losses. Near cities the voltage steps down in stages, finally hitting about 240 V before it reaches your home sockets. 🏠 :contentReference[oaicite:13]{index=13}

High-yield NEET nuggets 🏆

  1. The golden ratio \( v_s / v_p = N_s / N_p \)—know it cold for both rms and peak values. :contentReference[oaicite:14]{index=14}
  2. Power conservation in an ideal unit: \( i_p v_p = i_s v_s \). Expect questions that swap voltage for current. :contentReference[oaicite:15]{index=15}
  3. Identify step-up vs. step-down from the turns count or voltage ratio. 🔼🔽 :contentReference[oaicite:16]{index=16}
  4. Spot the four main energy losses (flux leakage, resistance, eddy currents, hysteresis) and how each fix works. 🔧 :contentReference[oaicite:17]{index=17}
  5. Explain why power grids transmit at high voltage—connect it to I2R loss reduction. 🌐 :contentReference[oaicite:18]{index=18}

Keep practicing problems—transformers often carry easy points on the exam. You’ve got this! 💪